Edit Profile (opens in new tab) Piatnitski, Andrey L. Co-Author Distance Author ID: piatnitski.andrey-l Published as: Piatnitski, Andrey; Piatnitski, A.; Pyatnitskij, A. L.; Piatnitski, Andrey L.; Piatnitski, A. L.; Piatnitski, Andrei L.; Pyatnitskiĭ, A. L.; Pyatnitskiĭ, Andreĭ L’vovich; Piatnitskii, A. L.; Pyatnitskii, A. L.; Piatniski, Andrey; Pyatniskii, A. L.; Piatnitskii, A. more...less Homepage: https://blogg.uit.no/api009/ Documents Indexed: 174 Publications since 1980, including 2 Books and 11 Additional arXiv Preprints 2 Contributions as Editor Co-Authors: 95 Co-Authors with 160 Joint Publications 3,434 Co-Co-Authors all top 5 Co-Authors 16 single-authored 25 Zhizhina, Elena Anatol’evna 18 Amaziane, Brahim 17 Pankratov, Leonid S. 15 Allaire, Grégoire 13 Chechkin, Gregory Aleksandrovich 12 Braides, Andrea 10 Kleptsyna, Marina L. 9 Mikelić, Andro 8 Bourgeat, Alain P. 8 Pankratova, Iryna L. 7 Pardoux, Etienne 7 Rybalko, Volodymyr 6 Chiadò Piat, Valeria 5 Kozlov, Sergeĭ Mikhaĭlovich 5 Popier, Alexandre 5 Shamaev, Alexei S. 4 Jurak, Mladen 4 Kondrat’yev, Yuriĭ Grygorovych 4 Kuksin, Sergeĭ B. 4 Lukkassen, Dag 4 Nazarov, Sergeĭ Aleksandrovich 3 Antontsev, Stanislav Nikolaevich 3 Borisov, Denis Ivanovich 3 Campillo, Fabien 3 Cioranescu, Doina 3 Dufrêche, Jean-François 3 Mathieu, Pierre 3 Meidell, Annette 3 Sloushch, Vladimir Anatolevich 3 Suslina, Tat’yana Aleksandrovna 3 Zhikov, Vasiliĭ Vasil’evich 2 Alicandro, Roberto 2 Amirat, Youcef Aït 2 Belyaev, Alexander G. 2 Bodart, Olivier 2 Brizzi, Robert 2 Capdeboscq, Yves 2 Damlamian, Alain 2 Donato, Patrizia 2 Ferreira, Rita 2 Gadyl’shin, Rustem R. 2 Iftimie, Bogdan 2 Marušić-Paloka, Eduard 2 Mascarenhas, Maria-Luisa 2 Molchanov, Stanislav Alekseevich 2 Panasenko, Grigory P. 2 Pirogov, Sergeĭ A. 2 Ptashnyk, Mariya 2 Rybalko, Antonina 2 Shirikyan, Armen R. 1 Alkhutov, Yuriy Alexandrovich 1 Ansini, Nadia 1 Astashova, Irina Viktorovna 1 Bogachev, Vladimir Igorevich 1 Cardone, Giuseppe 1 Causin, Andrea 1 Chueshov, Igor’ Dmitrievich 1 Cicalese, Marco 1 Craig, Walter 1 D’Apice, Ciro 1 De Luca, Lucia 1 De Maio, Umberto 1 Denisov, Vasiliĭ Nikolaevich 1 Diop, Mamadou Abdoul 1 Eliasson, L. Hakan 1 Engström, Jonas 1 Friedman, Avner 1 Gantert, Nina 1 Gaudiello, Antonio 1 Gilbert, Robert Pertsch 1 Grigor’yan, Alexander Asaturovich 1 Hairer, Martin 1 Heintz, Alexei G. 1 Huang, Guan 1 Jäger, Willy 1 Kappeler, Thomas 1 Kaßmann, Moritz 1 Kozlov, Valeriĭ Vasil’evich 1 Nadirashvili, Nikolai S. 1 Pastukhova, Svetlana Evgenievna 1 Persson, Lars-Erik 1 Pettersson, Irina 1 Remy, Elisabeth 1 Sadovnichiĭ, Viktor Antonovich 1 Shkalikov, Andreĭ Andreevich 1 Siess, Vincent 1 Solci, Margherita 1 Stëpin, Anatoliĭ Mikhaĭlovich 1 Tribuzio, Antonio 1 Vanninathan, Muthusamy 1 Vernescu, Bogdan 1 Wall, Peter 1 Wayne, Clarence Eugene 1 Yurinskiĭ, Vadim Vladimirovich 1 Zheng, Weian all top 5 Serials 7 Asymptotic Analysis 7 SIAM Journal on Mathematical Analysis 6 Applicable Analysis 6 Archive for Rational Mechanics and Analysis 6 Russian Mathematical Surveys 5 Journal of Differential Equations 5 Networks and Heterogeneous Media 4 Journal of Mathematical Analysis and Applications 4 Nonlinearity 4 Mathematics of the USSR, Sbornik 4 Stochastic Processes and their Applications 4 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 3 Communications in Mathematical Physics 3 Journal of Statistical Physics 3 Journal of Functional Analysis 3 Matematicheskiĭ Sbornik. Novaya Seriya 3 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 3 Journal de Mathématiques Pures et Appliquées. Neuvième Série 3 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 3 Journal of Mathematical Sciences (New York) 3 Nonlinear Analysis. Real World Applications 3 Discrete and Continuous Dynamical Systems. Series B 3 Multiscale Modeling & Simulation 2 Journal of Mathematical Physics 2 Mathematical Methods in the Applied Sciences 2 Uspekhi Matematicheskikh Nauk [N. S.] 2 Journal of the London Mathematical Society. Second Series 2 Communications in Partial Differential Equations 2 Izvestiya: Mathematics 2 Markov Processes and Related Fields 2 Stochastic and Partial Differential Equations. Analysis and Computations 1 Communications on Pure and Applied Mathematics 1 Moscow University Mathematics Bulletin 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Theory of Probability and its Applications 1 The Annals of Probability 1 Indiana University Mathematics Journal 1 Proceedings of the London Mathematical Society. Third Series 1 Siberian Mathematical Journal 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Physica D 1 Revista Matemática Iberoamericana 1 The Annals of Applied Probability 1 Glasnik Matematički. Serija III 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 SIAM Journal on Applied Mathematics 1 Vestnik Moskovskogo Universiteta. Seriya I. Matematika, Mekhanika 1 Matematicheskiĭ Sbornik 1 Russian Journal of Mathematical Physics 1 Sbornik: Mathematics 1 Doklady Mathematics 1 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 1 Fractional Calculus & Applied Analysis 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Computational Geosciences 1 Communications in Contemporary Mathematics 1 International Mathematical Journal 1 Portugaliae Mathematica. Nova Série 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Comptes Rendus. Mécanique. Académie des Sciences, Paris 1 Communications on Pure and Applied Analysis 1 Journal of Mathematical Physics, Analysis, Geometry 1 Complex Variables and Elliptic Equations 1 Translations of Mathematical Monographs 1 GAKUTO International Series. Mathematical Sciences and Applications 1 Annali dell’Università di Ferrara. Sezione VII. Scienze Matematiche 1 Advances in Calculus of Variations 1 S\(\vec{\text{e}}\)MA Journal 1 Izvestiya Irkutskogo Gosudarstvennogo Universiteta. Seriya Matematika 1 Pure and Applied Functional Analysis 1 SpringerBriefs on PDEs and Data Science all top 5 Fields 141 Partial differential equations (35-XX) 35 Probability theory and stochastic processes (60-XX) 33 Fluid mechanics (76-XX) 25 Mechanics of deformable solids (74-XX) 12 Integral equations (45-XX) 12 Calculus of variations and optimal control; optimization (49-XX) 10 Statistical mechanics, structure of matter (82-XX) 9 Operator theory (47-XX) 4 History and biography (01-XX) 3 Quantum theory (81-XX) 2 General and overarching topics; collections (00-XX) 2 Difference and functional equations (39-XX) 2 Integral transforms, operational calculus (44-XX) 2 Functional analysis (46-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Optics, electromagnetic theory (78-XX) 2 Biology and other natural sciences (92-XX) 1 Measure and integration (28-XX) 1 Ordinary differential equations (34-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Statistics (62-XX) 1 Geophysics (86-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 129 Publications have been cited 1,543 times in 989 Documents Cited by ▼ Year ▼ Approximations of effective coefficients in stochastic homogenization. Zbl 1058.35023 Bourgeat, Alain; Piatnitski, Andrey 94 2004 Homogenization. Methods and applications. Transl. from the Russian by Tamara Rozhkovskaya. Zbl 1128.35002 Chechkin, G. A.; Piatnitski, A. L.; Shamaev, A. S. 93 2007 Quenched invariance principles for random walks on percolation clusters. Zbl 1131.82012 Mathieu, P.; Piatnitski, A. 91 2007 The boundary-value problem in domains with very rapidly oscillating boundary. Zbl 0938.35049 Chechkin, Gregory A.; Friedman, Avner; Piatnitski, Andrey L. 66 1999 Homogenization of the Schrödinger equation and effective mass theorems. Zbl 1081.35092 Allaire, Grégoire; Piatnitski, Andrey 54 2005 Homogenization of random singular structures and random measures. Zbl 1113.35021 Zhikov, V. V.; Pyatniskii, A. L. 39 2006 Asymptotic behavior of a solution to a boundary value problem in a perforated domain with oscillating boundary. Zbl 0918.35043 Belyaev, A. G.; Pyatnitskij, A. L.; Chechkin, G. A. 33 1998 Periodic homogenization of nonlocal operators with a convolution-type kernel. Zbl 1356.45003 Piatnitski, A.; Zhizhina, E. 30 2017 Boundary homogenization in domains with randomly oscillating boundary. Zbl 1219.35021 Amirat, Youcef; Bodart, Olivier; Chechkin, Gregory A.; Piatnitski, Andrey L. 28 2011 Homogenization of surface and length energies for spin systems. Zbl 1270.35057 Braides, Andrea; Piatnitski, Andrey 27 2013 Homogenization of immiscible compressible two-phase flow in porous media: application to gas migration in a nuclear waste repository. Zbl 1215.35024 Amaziane, B.; Antontsev, S.; Pankratov, L.; Piatnitski, A. 26 2010 Homogenization of periodic systems with large potentials. Zbl 1072.35023 Allaire, Grégoire; Capdeboscq, Yves; Piatnitski, Andrey; Siess, Vincent; Vanninathan, M. 25 2004 Homogenization of boundary-value problem in a locally periodic perforated domain. Zbl 1030.35009 Chechkin, Gregory A.; Piatnitski, Andrey L. 25 1999 Homogenization approach to the dispersion theory for reactive transport through porous media. Zbl 1213.35057 Allaire, Grégoire; Mikelić, Andro; Piatnitski, Andrey 25 2010 Khasminskii-Whitham averaging for randomly perturbed KdV equation. Zbl 1148.35077 Kuksin, Sergei B.; Piatnitski, Andrey L. 24 2008 Asymptotic analysis and domain decomposition for a biharmonic problem in a thin multi-structure. Zbl 1347.35106 Gaudiello, Antonio; Panasenko, Grigory; Piatnitski, Andrey 24 2016 Averaging in a perforated domain with an oscillating third boundary condition. Zbl 1030.35008 Belyaev, A. G.; Pyatnitskij, A. L.; Chechkin, G. A. 22 2001 Homogenization of a nonlinear convection-diffusion equation with rapidly oscillating coefficients and strong convection. Zbl 1106.35006 Marušić-Paloka, Eduard; Piatnitski, Andrey L. 21 2005 Homogenization of a nonlinear random parabolic partial differential equation. Zbl 1075.35003 Pardoux, E.; Piatnitski, A. L. 21 2003 Homogenization of the linearized ionic transport equations in rigid periodic porous media. Zbl 1314.76039 Allaire, Grégoire; Mikelić, Andro; Piatnitski, Andrey 20 2010 Einstein relation for reversible diffusions in a random environment. Zbl 1264.60062 Gantert, Nina; Mathieu, Pierre; Piatnitski, Andrey 20 2012 Ion transport in porous media: derivation of the macroscopic equations using upscaling and properties of the effective coefficients. Zbl 1392.76071 Allaire, Grégoire; Brizzi, Robert; Dufrêche, Jean-François; Mikelić, Andro; Piatnitski, Andrey 17 2013 A variational approach to double-porosity problems. Zbl 1113.35014 Braides, Andrea; Chiadò Piat, Valeria; Piatnitski, Andrey 16 2004 Homogenization of elliptic difference operators. Zbl 1097.39501 Piatnitski, Andrey; Remy, Elisabeth 16 2001 Homogenization of random parabolic operator with large potential. Zbl 1099.35009 Campillo, Fabien; Kleptsyna, Marina; Piatnitski, Andrey 16 2001 Estimates in probability of the residual between the random and the homogenized solutions of one-dimensional second-order operator. Zbl 0960.60057 Bourgeat, A.; Piatnitski, A. 16 1999 Singular homogenization with stationary in time and periodic in space coefficients. Zbl 1113.35015 Diop, M. A.; Iftimie, B.; Pardoux, E.; Piatnitski, A. L. 16 2006 On the double porosity model of a single phase flow in random media. Zbl 1060.76113 Bourgeat, A.; Mikelić, A.; Piatnitski, A. 15 2003 A coupling approach to randomly forced nonlinear PDE’s. II. Zbl 1010.60066 Kuksin, Sergei; Piatniski, Andrey; Shirikyan, Armen 15 2002 Nonlinear flow through double porosity media in variable exponent Sobolev spaces. Zbl 1163.35410 Amaziane, B.; Pankratov, L.; Piatnitski, A. 15 2009 On homogenization of networks and junctions. Zbl 1031.35018 Chechkin, Gregory A.; Jikov, Vasili V.; Lukkassen, Dag; Piatnitski, Andrey L. 14 2002 Homogenization of a singular random one-dimensional PDE with time-varying coefficients. Zbl 1255.60108 Pardoux, Étienne; Piatnitski, Andrey 14 2012 Averaging of nonstationary parabolic operators with large lower order terms. Zbl 1201.35034 Donato, Patrizia; Piatnitski, Andrey 13 2006 Homogenization of nonlinear reaction-diffusion equation with a large reaction term. Zbl 1205.35019 Allaire, Grégoire; Piatnitski, Andrey 13 2010 Uniform spectral asymptotics for singularly perturbed locally periodic operators. Zbl 1026.35012 Allaire, Grégoire; Piatnitski, Andrey 12 2002 Averaging a transport equation with small diffusion and oscillating velocity. Zbl 1013.76069 Bourgeat, A.; Jurak, M.; Piatnitski, A. L. 12 2003 Steklov problems in perforated domains with a coefficient of indefinite sign. Zbl 1262.35025 Piat, Valeria Chiado; Nazarov, Sergey S.; Piatnitski, Andrey 12 2012 Homogenization of a single-phase flow through a porous medium in a thin layer. Zbl 1154.76052 Amaziane, B.; Pankratov, L.; Piatnitski, A. 12 2007 Homogenization of Lévy-type operators with oscillating coefficients. Zbl 1434.45001 Kassmann, M.; Piatnitski, A.; Zhizhina, E. 12 2019 Asymptotics of a spectral-sieve problem. Zbl 1332.35235 Amirat, Youcef; Bodart, Olivier; Chechkin, Gregory A.; Piatnitski, Andrey L. 11 2016 Homogenization of a random non-stationary convection-diffusion problem. Zbl 1073.35023 Kleptsyna, M. L.; Pyatnitskiĭ, A. L. 11 2002 Hölder estimates for solutions of parabolic SPDEs. Zbl 1038.60058 Kuksin, S. B.; Nadirashvili, N. S.; Pyatnitskij, A. L. 11 2002 Homogenization of discrete high-contrast energies. Zbl 1321.49023 Braides, Andrea; Chiadò Piat, Valeria; Piatnitski, Andrey 11 2015 On the effective interfacial resistance through rough surfaces. Zbl 1207.35047 Donato, Patrizia; Piatnitski, Andrey 11 2010 \(\varGamma \)-convergence and homogenization of functionals in Sobolev spaces with variable exponents. Zbl 1357.49052 Amaziane, B.; Antontsev, S.; Pankratov, L.; Piatnitski, A. 11 2008 Homogenization of immiscible compressible two-phase flow in highly heterogeneous porous media with discontinuous capillary pressures. Zbl 1293.35025 Amaziane, Brahim; Pankratov, Leonid; Piatnitski, Andrey 10 2014 Asymptotic analysis of the Poisson-Boltzmann equation describing electrokinetics in porous media. Zbl 1264.35159 Allaire, Grégoire; Dufrêche, Jean-François; Mikelić, Andro; Piatnitski, Andrey 10 2013 Variational problems with percolation: dilute spin systems at zero temperature. Zbl 1260.82043 Braides, Andrea; Piatnitski, Andrey 10 2012 Random double porosity model. (Modèle de double porosité aléatoire.) Zbl 1024.35008 Bourgeat, Alain; Mikelić, Andro; Piatnitski, Andrey 10 1998 Asymptotic behavior of the ground state of singularly perturbed elliptic equations. Zbl 0937.58023 Piatnitski, Andrey L. 10 1998 Role of non-ideality for the ion transport in porous media: derivation of the macroscopic equations using upscaling. Zbl 1349.76803 Allaire, Grégoire; Brizzi, Robert; Dufrêche, Jean-François; Mikelić, Andro; Piatnitski, Andrey 10 2014 A variational theory of convolution-type functionals. Zbl 1528.49001 Alicandro, Roberto; Ansini, Nadia; Braides, Andrea; Piatnitski, Andrey; Tribuzio, Antonio 10 2023 Spectral analysis in thin tubes with axial heterogeneities. Zbl 1342.35197 Ferreira, Rita; Mascarenhas, M. Luísa; Piatnitski, Andrey 9 2015 Singular double porosity model. Zbl 1290.35195 Bourgeat, Alain; Chechkin, Gregory A.; Piatnitski, Andrey L. 9 2003 The existence of weak solutions to immiscible compressible two-phase flow in porous media: the case of fields with different rock-types. Zbl 1387.76098 Amaziane, Brahim; Pankratov, Leonid; Piatnitski, Andrey 9 2013 Homogenization of a singular random one-dimensional PDE. Zbl 1172.74043 Iftimie, Bogdan; Pardoux, Étienne; Piatnitski, Andrey 9 2008 On boundary value problem with singular inhomogeneity concentrated on the boundary. Zbl 1277.35142 Chechkin, G. A.; Cioranescu, D.; Damlamian, A.; Piatnitski, A. L. 9 2012 Averaging of a singular random source term in a diffusion convection equation. Zbl 1228.35029 Bourgeat, Alain; Piatnitski, Andrey L. 9 2010 Random homogenisation of a highly oscillatory singular potential. Zbl 1323.35230 Hairer, Martin; Pardoux, Etienne; Piatnitski, Andrey 8 2013 Homogenization of biomechanical models for plant tissues. Zbl 1383.35019 Piatnitski, Andrey; Ptashnyk, Mariya 8 2017 Stochastic homogenization of convolution type operators. Zbl 1433.35006 Piatnitski, A.; Zhizhina, E. 8 2020 On the behaviour at infinity of solutions to stationary convection-diffusion equation in a cylinder. Zbl 1178.35157 Pankratova, Iryna; Piatnitski, Andrey 8 2009 Homogenization of \(p\)-Laplacian in perforated domain. Zbl 1182.35017 Amaziane, B.; Antontsev, S.; Pankratov, L.; Piatnitski, A. 8 2009 Homogenization of the spectral problem for periodic elliptic operators with sign-changing density function. Zbl 1229.35159 Nazarov, Sergey A.; Pankratova, Iryna L.; Piatnitski, Andrey L. 8 2011 Homogenization and concentration for a diffusion equation with large convection in a bounded domain. Zbl 1233.35013 Allaire, G.; Pankratova, I.; Piatnitski, A. 8 2012 \(\Gamma \)-convergence approach to variational problems in perforated domains with Fourier boundary conditions. Zbl 1188.35015 Piat, Valeria Chiadò; Piatnitski, Andrey 8 2010 Homogenization of biomechanical models of plant tissues with randomly distributed cells. Zbl 1453.35017 Piatnitski, Andrey; Ptashnyk, Mariya 8 2020 On the asymptotic behaviour of eigenvalues of a boundary-value problem in a planar domain of Steklov sieve type. Zbl 1406.35032 Gadyl’shin, R. R.; Piatnitskii, A. L.; Chechkin, G. A. 8 2018 Topological singularities in periodic media: Ginzburg-Landau and core-radius approaches. Zbl 1481.35148 Alicandro, Roberto; Braides, Andrea; Cicalese, Marco; De Luca, Lucia; Piatnitski, Andrey 8 2022 Pointwise estimates for heat kernels of convolution-type operators. Zbl 06968912 Grigor’yan, Alexander; Kondratiev, Yuri; Piatnitski, Andrey; Zhizhina, Elena 7 2018 Steady states, fluctuation-dissipation theorems and homogenization for reversible diffusions in a random environment. Zbl 1408.35235 Mathieu, P.; Piatnitski, A. 7 2018 Homogenization of a singular random one-dimensional PDE. Zbl 1201.35036 Pardoux, Etienne; Piatnitski, Andrey 7 2006 Homogenization of random convolution energies. Zbl 1472.35027 Braides, Andrea; Piatnitski, Andrey 7 2021 Resolvent bounds for jump generators. Zbl 07327314 Kondratiev, Yuri; Molchanov, Stanislav; Piatnitski, Andrey; Zhizhina, Elena 7 2018 Overall properties of a discrete membrane with randomly distributed defects. Zbl 1147.74039 Braides, Andrea; Piatnitski, Andrey 7 2008 An existence result for nonisothermal immiscible incompressible 2-phase flow in heterogeneous porous media. Zbl 1384.35078 Amaziane, Brahim; Jurak, Mladen; Pankratov, Leonid; Piatnitski, Andrey 7 2017 On the rate of convergence of solutions in domain with random multilevel oscillating boundary. Zbl 1305.35019 Chechkin, G. A.; D’Apice, C.; De Maio, U.; Piatnitski, A. L. 6 2014 Localization effect for a spectral problem in a perforated domain with Fourier boundary conditions. Zbl 1276.35022 Chiadò Piat, V.; Pankratova, I.; Piatnitski, A. 6 2013 Homogenization in perforated domains with rapidly pulsing perforations. Zbl 1065.35044 Cioranescu, Doina; Piatnitski, Andrey L. 6 2003 Homogenization of a class of quasilinear elliptic equations in high-contrast fissured media. Zbl 1123.35307 Amaziane, B.; Pankratov, L.; Piatnitski, A. 6 2006 Homogenization of random degenerated nonlinear monotone operators. Zbl 1118.35003 Engström, J.; Persson, L.-E.; Piatnitski, A.; Wall, P. 6 2006 Homogenization of quadratic convolution energies in periodically perforated domains. Zbl 1500.35020 Braides, Andrea; Piatnitski, Andrey 6 2022 Averaging a singularly perturbed equation with rapidly oscillating coefficients in a layer. Zbl 0551.35025 Pyatnitskij, A. L. 5 1984 Homogenization of biased convolution type operators. Zbl 1474.45028 Piatnitski, A.; Zhizhina, E. 5 2019 An improved homogenization result for immiscible compressible two-phase flow in porous media. Zbl 1361.35019 Amaziane, Brahim; Pankratov, Leonid; Piatnitski, Andrey 5 2017 Homogenization of random parabolic operators. Zbl 0892.35019 Kleptsyna, M.; Piatnitski, A. 5 1995 On operator estimates in homogenization of nonlocal operators of convolution type. Zbl 1509.35030 Piatnitski, A.; Sloushch, V.; Suslina, T.; Zhizhina, E. 5 2023 Homogenization of the spectral Dirichlet problem for a system of differential equations with rapidly oscillating coefficients and changing sign density. Zbl 1221.35258 Nazarov, S. A.; Pyatnitskii, A. L. 5 2010 Homogenization of a porous medium with randomly pulsating microstructure. Zbl 1187.35009 Cioranescu, Doina; Piatnitski, Andrey 5 2006 Homogenization of convection-diffusion equation in infinite cylinder. Zbl 1262.35024 Pankratova, Iryna; Piatnitski, Andrey 5 2011 Homogenization of boundary value problems for monotone operators in perforated domains with rapidly oscillating boundary conditions of Fourier type. Zbl 1290.35019 Piatnitski, A.; Rybalko, V. 4 2011 Homogenization and localization with an interface. Zbl 1073.35018 Allaire, Grégoire; Capdeboscq, Yves; Piatnitski, Andrey 4 2003 Homogenization of a convection-diffusion equation in a thin rod structure. Zbl 1200.35023 Panasenko, G.; Pankratova, I.; Piatnitski, A. 4 2010 Scaling up of an underground nuclear waste repository including a possibly damaged zone. Zbl 1200.35309 Bourgeat, Alain; Marušić-Paloka, Eduard; Piatnitski, Andrey 4 2010 Nonlinear “double porosity” type model. Zbl 1016.76087 Pankratov, Leonid; Piatnitski, Andrey 4 2002 On the rate of convergence for perforated plates with a small interior Dirichlet zone. Zbl 1264.74189 Cardone, G.; Nazarov, S. A.; Piatnitski, A. L. 4 2011 Homogenized model of reaction-diffusion in a porous medium. Zbl 1187.76744 Pankratov, Leonid; Piatnitski, Andrey; Rybalko, Volodymyr 4 2003 Homogenization of nonisothermal immiscible incompressible two-phase flow in porous media. Zbl 1394.35028 Amaziane, B.; Jurak, M.; Pankratov, L.; Piatnitski, A. 3 2018 Homogenization of a nonstationary convection-diffusion equation in a thin rod and in a layer. Zbl 1310.35026 Allaire, G.; Pankratova, I.; Piatnitski, A. 3 2012 Ground states of singularly perturbed convection-diffusion equation with oscillating coefficients. Zbl 1320.35050 Piatnitski, A.; Rybalko, A.; Rybalko, V. 3 2014 A variational theory of convolution-type functionals. Zbl 1528.49001 Alicandro, Roberto; Ansini, Nadia; Braides, Andrea; Piatnitski, Andrey; Tribuzio, Antonio 10 2023 On operator estimates in homogenization of nonlocal operators of convolution type. Zbl 1509.35030 Piatnitski, A.; Sloushch, V.; Suslina, T.; Zhizhina, E. 5 2023 Topological singularities in periodic media: Ginzburg-Landau and core-radius approaches. Zbl 1481.35148 Alicandro, Roberto; Braides, Andrea; Cicalese, Marco; De Luca, Lucia; Piatnitski, Andrey 8 2022 Homogenization of quadratic convolution energies in periodically perforated domains. Zbl 1500.35020 Braides, Andrea; Piatnitski, Andrey 6 2022 Homogenization of ferromagnetic energies on Poisson random sets in the plane. Zbl 1485.49019 Braides, Andrea; Piatnitski, Andrey 3 2022 Spectrum of a convolution operator with potential. Zbl 1544.47068 Borisov, Denis I.; Zhizhina, Elena A.; Piatnitski, Andrey L. 1 2022 Symptotic decomposition of solutions to parabolic equations with a random microstructure. Zbl 1500.35023 Kleptsyna, Marina; Piatnitski, Andrey; Popier, Alexandre 1 2022 Homogenization of random convolution energies. Zbl 1472.35027 Braides, Andrea; Piatnitski, Andrey 7 2021 Homogenization of immiscible compressible two-phase flow in random porous media. Zbl 1477.35018 Amaziane, B.; Pankratov, L.; Piatnitski, A. 1 2021 Stochastic homogenization of convolution type operators. Zbl 1433.35006 Piatnitski, A.; Zhizhina, E. 8 2020 Homogenization of biomechanical models of plant tissues with randomly distributed cells. Zbl 1453.35017 Piatnitski, Andrey; Ptashnyk, Mariya 8 2020 Homogenization of Lévy-type operators with oscillating coefficients. Zbl 1434.45001 Kassmann, M.; Piatnitski, A.; Zhizhina, E. 12 2019 Homogenization of biased convolution type operators. Zbl 1474.45028 Piatnitski, A.; Zhizhina, E. 5 2019 Limit behaviour of diffusion in high-contrast periodic media and related Markov. Zbl 1409.60041 Piatnitski, Andrey; Pirogov, S.; Zhizhina, E. 1 2019 On the behaviour at infinity of solutions to nonlocal parabolic type problems. Zbl 1439.35192 Zhizhina, Elena Anatol’evna; Pyatnitskiĭ, Andreĭ L’vovich 1 2019 On the asymptotic behaviour of eigenvalues of a boundary-value problem in a planar domain of Steklov sieve type. Zbl 1406.35032 Gadyl’shin, R. R.; Piatnitskii, A. L.; Chechkin, G. A. 8 2018 Pointwise estimates for heat kernels of convolution-type operators. Zbl 06968912 Grigor’yan, Alexander; Kondratiev, Yuri; Piatnitski, Andrey; Zhizhina, Elena 7 2018 Steady states, fluctuation-dissipation theorems and homogenization for reversible diffusions in a random environment. Zbl 1408.35235 Mathieu, P.; Piatnitski, A. 7 2018 Resolvent bounds for jump generators. Zbl 07327314 Kondratiev, Yuri; Molchanov, Stanislav; Piatnitski, Andrey; Zhizhina, Elena 7 2018 Homogenization of nonisothermal immiscible incompressible two-phase flow in porous media. Zbl 1394.35028 Amaziane, B.; Jurak, M.; Pankratov, L.; Piatnitski, A. 3 2018 Asymptotic behaviour of ground states for mixtures of ferromagnetic and antiferromagnetic interactions in a dilute regime. Zbl 1395.82038 Braides, Andrea; Causin, Andrea; Piatnitski, Andrey; Solci, Margherita 1 2018 Stationary convection-diffusion equation in an infinite cylinder. Zbl 1383.35018 Pettersson, Irina; Piatnitski, Andrey 1 2018 Periodic homogenization of nonlocal operators with a convolution-type kernel. Zbl 1356.45003 Piatnitski, A.; Zhizhina, E. 30 2017 Homogenization of biomechanical models for plant tissues. Zbl 1383.35019 Piatnitski, Andrey; Ptashnyk, Mariya 8 2017 An existence result for nonisothermal immiscible incompressible 2-phase flow in heterogeneous porous media. Zbl 1384.35078 Amaziane, Brahim; Jurak, Mladen; Pankratov, Leonid; Piatnitski, Andrey 7 2017 An improved homogenization result for immiscible compressible two-phase flow in porous media. Zbl 1361.35019 Amaziane, Brahim; Pankratov, Leonid; Piatnitski, Andrey 5 2017 On the asymptotic behaviour of the kernel of an adjoint convection-diffusion operator in a long cylinder. Zbl 1382.35020 Allaire, Grégoire; Piatnitski, Andrey 2 2017 Scaling limit of symmetric random walk in high-contrast periodic environment. Zbl 1382.82021 Piatnitski, A.; Zhizhina, E. 2 2017 Asymptotic analysis and domain decomposition for a biharmonic problem in a thin multi-structure. Zbl 1347.35106 Gaudiello, Antonio; Panasenko, Grigory; Piatnitski, Andrey 24 2016 Asymptotics of a spectral-sieve problem. Zbl 1332.35235 Amirat, Youcef; Bodart, Olivier; Chechkin, Gregory A.; Piatnitski, Andrey L. 11 2016 Spectral problem with Steklov condition on a thin perforated interface. Zbl 1341.35093 Gadyl’shin, R. R.; Piatnitski, Andrey L.; Chechkin, G. A. 2 2016 On the first eigenpair of singularly perturbed operators with oscillating coefficients. Zbl 1339.35199 Piatnitski, A.; Rybalko, V. 1 2016 Homogenization of discrete high-contrast energies. Zbl 1321.49023 Braides, Andrea; Chiadò Piat, Valeria; Piatnitski, Andrey 11 2015 Spectral analysis in thin tubes with axial heterogeneities. Zbl 1342.35197 Ferreira, Rita; Mascarenhas, M. Luísa; Piatnitski, Andrey 9 2015 Homogenization of random parabolic operators. Diffusion approximation. Zbl 1364.35032 Kleptsyna, M.; Piatnitski, A.; Popier, A. 2 2015 Homogenization of immiscible compressible two-phase flow in highly heterogeneous porous media with discontinuous capillary pressures. Zbl 1293.35025 Amaziane, Brahim; Pankratov, Leonid; Piatnitski, Andrey 10 2014 Role of non-ideality for the ion transport in porous media: derivation of the macroscopic equations using upscaling. Zbl 1349.76803 Allaire, Grégoire; Brizzi, Robert; Dufrêche, Jean-François; Mikelić, Andro; Piatnitski, Andrey 10 2014 On the rate of convergence of solutions in domain with random multilevel oscillating boundary. Zbl 1305.35019 Chechkin, G. A.; D’Apice, C.; De Maio, U.; Piatnitski, A. L. 6 2014 Ground states of singularly perturbed convection-diffusion equation with oscillating coefficients. Zbl 1320.35050 Piatnitski, A.; Rybalko, A.; Rybalko, V. 3 2014 Homogenization of surface and length energies for spin systems. Zbl 1270.35057 Braides, Andrea; Piatnitski, Andrey 27 2013 Ion transport in porous media: derivation of the macroscopic equations using upscaling and properties of the effective coefficients. Zbl 1392.76071 Allaire, Grégoire; Brizzi, Robert; Dufrêche, Jean-François; Mikelić, Andro; Piatnitski, Andrey 17 2013 Asymptotic analysis of the Poisson-Boltzmann equation describing electrokinetics in porous media. Zbl 1264.35159 Allaire, Grégoire; Dufrêche, Jean-François; Mikelić, Andro; Piatnitski, Andrey 10 2013 The existence of weak solutions to immiscible compressible two-phase flow in porous media: the case of fields with different rock-types. Zbl 1387.76098 Amaziane, Brahim; Pankratov, Leonid; Piatnitski, Andrey 9 2013 Random homogenisation of a highly oscillatory singular potential. Zbl 1323.35230 Hairer, Martin; Pardoux, Etienne; Piatnitski, Andrey 8 2013 Localization effect for a spectral problem in a perforated domain with Fourier boundary conditions. Zbl 1276.35022 Chiadò Piat, V.; Pankratova, I.; Piatnitski, A. 6 2013 Einstein relation for reversible diffusions in a random environment. Zbl 1264.60062 Gantert, Nina; Mathieu, Pierre; Piatnitski, Andrey 20 2012 Homogenization of a singular random one-dimensional PDE with time-varying coefficients. Zbl 1255.60108 Pardoux, Étienne; Piatnitski, Andrey 14 2012 Steklov problems in perforated domains with a coefficient of indefinite sign. Zbl 1262.35025 Piat, Valeria Chiado; Nazarov, Sergey S.; Piatnitski, Andrey 12 2012 Variational problems with percolation: dilute spin systems at zero temperature. Zbl 1260.82043 Braides, Andrea; Piatnitski, Andrey 10 2012 On boundary value problem with singular inhomogeneity concentrated on the boundary. Zbl 1277.35142 Chechkin, G. A.; Cioranescu, D.; Damlamian, A.; Piatnitski, A. L. 9 2012 Homogenization and concentration for a diffusion equation with large convection in a bounded domain. Zbl 1233.35013 Allaire, G.; Pankratova, I.; Piatnitski, A. 8 2012 Homogenization of a nonstationary convection-diffusion equation in a thin rod and in a layer. Zbl 1310.35026 Allaire, G.; Pankratova, I.; Piatnitski, A. 3 2012 Spectral analysis in a thin domain with periodically oscillating characteristics. Zbl 1248.35135 Ferreira, Rita; Mascarenhas, Luísa M.; Piatnitski, Andrey 1 2012 Boundary homogenization in domains with randomly oscillating boundary. Zbl 1219.35021 Amirat, Youcef; Bodart, Olivier; Chechkin, Gregory A.; Piatnitski, Andrey L. 28 2011 Homogenization of the spectral problem for periodic elliptic operators with sign-changing density function. Zbl 1229.35159 Nazarov, Sergey A.; Pankratova, Iryna L.; Piatnitski, Andrey L. 8 2011 Homogenization of convection-diffusion equation in infinite cylinder. Zbl 1262.35024 Pankratova, Iryna; Piatnitski, Andrey 5 2011 Homogenization of boundary value problems for monotone operators in perforated domains with rapidly oscillating boundary conditions of Fourier type. Zbl 1290.35019 Piatnitski, A.; Rybalko, V. 4 2011 On the rate of convergence for perforated plates with a small interior Dirichlet zone. Zbl 1264.74189 Cardone, G.; Nazarov, S. A.; Piatnitski, A. L. 4 2011 Homogenization of spectral problem for locally periodic elliptic operators with sign-changing density function. Zbl 1222.35021 Pankratova, I.; Piatnitski, A. 2 2011 Erratum: “Homogenization of the linearized ionic transport equations in rigid periodic porous media” [J. Math. Phys. 51, 123103, 18 p. (2010)]. Zbl 1317.76075 Allaire, Grégoire; Mikelić, Andro; Piatnitski, Andrey 1 2011 Homogenization of immiscible compressible two-phase flow in porous media: application to gas migration in a nuclear waste repository. Zbl 1215.35024 Amaziane, B.; Antontsev, S.; Pankratov, L.; Piatnitski, A. 26 2010 Homogenization approach to the dispersion theory for reactive transport through porous media. Zbl 1213.35057 Allaire, Grégoire; Mikelić, Andro; Piatnitski, Andrey 25 2010 Homogenization of the linearized ionic transport equations in rigid periodic porous media. Zbl 1314.76039 Allaire, Grégoire; Mikelić, Andro; Piatnitski, Andrey 20 2010 Homogenization of nonlinear reaction-diffusion equation with a large reaction term. Zbl 1205.35019 Allaire, Grégoire; Piatnitski, Andrey 13 2010 On the effective interfacial resistance through rough surfaces. Zbl 1207.35047 Donato, Patrizia; Piatnitski, Andrey 11 2010 Averaging of a singular random source term in a diffusion convection equation. Zbl 1228.35029 Bourgeat, Alain; Piatnitski, Andrey L. 9 2010 \(\Gamma \)-convergence approach to variational problems in perforated domains with Fourier boundary conditions. Zbl 1188.35015 Piat, Valeria Chiadò; Piatnitski, Andrey 8 2010 Homogenization of the spectral Dirichlet problem for a system of differential equations with rapidly oscillating coefficients and changing sign density. Zbl 1221.35258 Nazarov, S. A.; Pyatnitskii, A. L. 5 2010 Homogenization of a convection-diffusion equation in a thin rod structure. Zbl 1200.35023 Panasenko, G.; Pankratova, I.; Piatnitski, A. 4 2010 Scaling up of an underground nuclear waste repository including a possibly damaged zone. Zbl 1200.35309 Bourgeat, Alain; Marušić-Paloka, Eduard; Piatnitski, Andrey 4 2010 Homogenization of variational functionals with nonstandard growth in perforated domains. Zbl 1262.35017 Amaziane, Brahim; Pankratov, Leonid; Piatnitski, Andrey 2 2010 Nonlinear flow through double porosity media in variable exponent Sobolev spaces. Zbl 1163.35410 Amaziane, B.; Pankratov, L.; Piatnitski, A. 15 2009 On the behaviour at infinity of solutions to stationary convection-diffusion equation in a cylinder. Zbl 1178.35157 Pankratova, Iryna; Piatnitski, Andrey 8 2009 Homogenization of \(p\)-Laplacian in perforated domain. Zbl 1182.35017 Amaziane, B.; Antontsev, S.; Pankratov, L.; Piatnitski, A. 8 2009 Khasminskii-Whitham averaging for randomly perturbed KdV equation. Zbl 1148.35077 Kuksin, Sergei B.; Piatnitski, Andrey L. 24 2008 \(\varGamma \)-convergence and homogenization of functionals in Sobolev spaces with variable exponents. Zbl 1357.49052 Amaziane, B.; Antontsev, S.; Pankratov, L.; Piatnitski, A. 11 2008 Homogenization of a singular random one-dimensional PDE. Zbl 1172.74043 Iftimie, Bogdan; Pardoux, Étienne; Piatnitski, Andrey 9 2008 Overall properties of a discrete membrane with randomly distributed defects. Zbl 1147.74039 Braides, Andrea; Piatnitski, Andrey 7 2008 Homogenization. Methods and applications. Transl. from the Russian by Tamara Rozhkovskaya. Zbl 1128.35002 Chechkin, G. A.; Piatnitski, A. L.; Shamaev, A. S. 93 2007 Quenched invariance principles for random walks on percolation clusters. Zbl 1131.82012 Mathieu, P.; Piatnitski, A. 91 2007 Homogenization of a single-phase flow through a porous medium in a thin layer. Zbl 1154.76052 Amaziane, B.; Pankratov, L.; Piatnitski, A. 12 2007 Homogenization of random singular structures and random measures. Zbl 1113.35021 Zhikov, V. V.; Pyatniskii, A. L. 39 2006 Singular homogenization with stationary in time and periodic in space coefficients. Zbl 1113.35015 Diop, M. A.; Iftimie, B.; Pardoux, E.; Piatnitski, A. L. 16 2006 Averaging of nonstationary parabolic operators with large lower order terms. Zbl 1201.35034 Donato, Patrizia; Piatnitski, Andrey 13 2006 Homogenization of a singular random one-dimensional PDE. Zbl 1201.35036 Pardoux, Etienne; Piatnitski, Andrey 7 2006 Homogenization of a class of quasilinear elliptic equations in high-contrast fissured media. Zbl 1123.35307 Amaziane, B.; Pankratov, L.; Piatnitski, A. 6 2006 Homogenization of random degenerated nonlinear monotone operators. Zbl 1118.35003 Engström, J.; Persson, L.-E.; Piatnitski, A.; Wall, P. 6 2006 Homogenization of a porous medium with randomly pulsating microstructure. Zbl 1187.35009 Cioranescu, Doina; Piatnitski, Andrey 5 2006 Homogenization of quasilinear elliptic equations with non-uniformly bounded coefficients. Zbl 1117.35303 Amaziane, Brahim; Pankratov, Leonid; Piatnitski, Andrey 1 2006 Homogenization of the Schrödinger equation and effective mass theorems. Zbl 1081.35092 Allaire, Grégoire; Piatnitski, Andrey 54 2005 Homogenization of a nonlinear convection-diffusion equation with rapidly oscillating coefficients and strong convection. Zbl 1106.35006 Marušić-Paloka, Eduard; Piatnitski, Andrey L. 21 2005 Approximations of effective coefficients in stochastic homogenization. Zbl 1058.35023 Bourgeat, Alain; Piatnitski, Andrey 94 2004 Homogenization of periodic systems with large potentials. Zbl 1072.35023 Allaire, Grégoire; Capdeboscq, Yves; Piatnitski, Andrey; Siess, Vincent; Vanninathan, M. 25 2004 A variational approach to double-porosity problems. Zbl 1113.35014 Braides, Andrea; Chiadò Piat, Valeria; Piatnitski, Andrey 16 2004 Homogenization of a nonlinear random parabolic partial differential equation. Zbl 1075.35003 Pardoux, E.; Piatnitski, A. L. 21 2003 On the double porosity model of a single phase flow in random media. Zbl 1060.76113 Bourgeat, A.; Mikelić, A.; Piatnitski, A. 15 2003 Averaging a transport equation with small diffusion and oscillating velocity. Zbl 1013.76069 Bourgeat, A.; Jurak, M.; Piatnitski, A. L. 12 2003 Singular double porosity model. Zbl 1290.35195 Bourgeat, Alain; Chechkin, Gregory A.; Piatnitski, Andrey L. 9 2003 Homogenization in perforated domains with rapidly pulsing perforations. Zbl 1065.35044 Cioranescu, Doina; Piatnitski, Andrey L. 6 2003 Homogenization and localization with an interface. Zbl 1073.35018 Allaire, Grégoire; Capdeboscq, Yves; Piatnitski, Andrey 4 2003 ...and 29 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,160 Authors 66 Piatnitski, Andrey L. 38 Chechkin, Gregory Aleksandrovich 25 Pankratov, Leonid S. 24 Braides, Andrea 23 Allaire, Grégoire 23 Amaziane, Brahim 15 Legoll, Frédéric 14 Mel’nyk, Taras A. 13 Muntean, Adrian 13 Zhizhina, Elena Anatol’evna 12 Heida, Martin 12 Kumagai, Takashi 12 Le Bris, Claude 12 Nazarov, Sergeĭ Aleksandrovich 12 Pereira, Marcone Corrêa 11 Bekmaganbetov, Kuanysh Abdrakhmanovich 11 Faggionato, Alessandra 11 Mikelić, Andro 10 Borisov, Denis Ivanovich 10 Cicalese, Marco 10 Jurak, Mladen 10 Kuksin, Sergeĭ B. 10 Pardoux, Etienne 9 Amirat, Youcef Aït 9 Cardone, Giuseppe 9 Chepyzhov, Vladimir V. 9 Duan, Jinqiao 9 Gaudiello, Antonio 9 Gloria, Antoine 9 Neukamm, Stefan 9 Otto, Felix 9 Shaposhnikova, Tatiana A. 8 Bunoiu, Renata 8 Gadyl’shin, Rustem R. 8 Neuss-Radu, Maria 8 Ruf, Matthias 8 Souganidis, Panagiotis E. 8 Timofte, Claudia 7 Anza Hafsa, Omar 7 Cao, Liqun 7 Chechkina, Aleksandra Grigorievna 7 Deuschel, Jean-Dominique 7 Gu, Yu 7 Hairer, Martin 7 Khludnev, Aleksandr Mikhaĭlovich 7 Kovtunenko, Viktor Anatolievich 7 Mandallena, Jean-Philippe 7 Sili, Ali 7 Solci, Margherita 7 Suslina, Tat’yana Aleksandrovna 6 Abdulle, Assyr 6 Bal, Guillaume 6 Berger, Noam 6 Biskup, Marek 6 Efendiev, Yalchin R. 6 Fernández Bonder, Julián 6 Fribergh, Alexander 6 Gahn, Markus 6 Koroleva, Yulia O. 6 Mourrat, Jean-Christophe 6 Pankratova, Iryna L. 6 Ptashnyk, Mariya 6 Wang, Jian 6 Wei, Jinlong 6 Woukeng, Jean Louis 6 Zeppieri, Caterina Ida 6 Zhan, Huashui 5 Bach, Annika 5 Barlow, Martin T. 5 Beneš, Michal 5 Chechkina, Tatiana P. 5 Chen, Xin 5 Chung, Tsz Shun Eric 5 De Maio, Umberto 5 Leung, Wingtat 5 Mathieu, Pierre 5 Nakasato, Jean Carlos 5 Orlando, Gianluca 5 Panasenko, Grigory P. 5 Pažanin, Igor 5 Perugia, Carmen 5 Pettersson, Klas 5 Pop, Iuliu Sorin 5 Schmuck, Markus 5 Schweizer, Ben 5 Shumilova, Vladlena Valerievna 5 Slowik, Martin 5 Varga, Mario 5 Wheeler, Mary Fanett 5 Zubkova, Anna V. 4 Aiyappan, Srinivasan 4 Andres, Sebastian 4 Arrieta, José M. 4 Boivin, Daniel 4 Brown, Donald L. 4 Cancès, Eric 4 Cerrai, Sandra 4 Dal Maso, Gianni 4 D’Apice, Ciro 4 Dario, Paul ...and 1,060 more Authors all top 5 Cited in 224 Serials 46 Applicable Analysis 30 Mathematical Methods in the Applied Sciences 28 SIAM Journal on Mathematical Analysis 27 Multiscale Modeling & Simulation 26 Journal of Mathematical Sciences (New York) 25 Journal of Mathematical Analysis and Applications 24 Journal of Differential Equations 22 Stochastic Processes and their Applications 21 The Annals of Probability 20 Nonlinear Analysis. 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