# zbMATH — the first resource for mathematics

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 Documents Indexed: 627 Publications since 1959, including 41 Books Biographic References: 17 Publications
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#### Co-Authors

 119 single-authored 78 Plamenevskiĭ, Boris Alekseevich 48 Shaposhnikova, Tatyana Olegovna 46 Kozlov, Vladimir A. 35 Kresin, Gershon I. 31 Nazarov, Sergeĭ Aleksandrovich 27 Schmidt, Gunther 20 Movchan, Alexander B. 20 Rossmann, Jürgen 18 Lanzara, Flavia 16 Cianchi, Andrea 15 Poborchii, S. V. 14 Khavin, Viktor Petrovich 14 Solov’ev, Alexander Artemovich 12 Vaĭnberg, Boris Rufimovich 11 Verbitsky, Igor E. 9 Gel’man, Igor’ Vol’fovich 9 Kuznetsov, Nikolai Germanovich 8 Cialdea, Alberto 8 Grachev, Nikolai V. 6 McOwen, Robert C. 5 Burago, Yuriĭ Dmitrievich 5 Karlin, Vladimir 5 Khajkin, Yu. E. 5 Mayboroda, Svitlana 5 Mitrea, Marius 5 Sapozhnikova, V. D. 5 Slutskiĭ, A. S. 4 Krol’, I. N. 4 Paneah, Boris 4 Shubin, Mikhail Aleksandrovich 4 Verzhbinskij, G. M. 4 Zargaryan, Stepan S. 3 Filippas, Stathis 3 Fomin, A. V. 3 Kerimov, T. M. 3 Kondrat’ev, Vladimir Aleksandrovich 3 Kuchment, Peter A. 3 Luo, Guo 3 Morozov, Nikita Fedorovich 3 Neves, Mario jun. 3 Nieves, Michael 3 Novruzov, Ali A. 3 Parton, Vladimir Z. 3 Poborchi, Sergei V. 3 Poborchi, Sergej V. 3 Tertikas, Achilles 3 Wendland, Wolfgang L. 2 Alvarado, Ryan 2 Babich, Vasiliĭ Mikhaĭlovich 2 Bakel’man, Il’ya Yakovlevich 2 Braverman, Maxim 2 Brigham, Dan 2 Donchev, Tzanko Donchev 2 Galaktionov, Victor Aleksandrovich 2 Gamkrelidze, Revaz Valerianovich 2 Gelman, I. W. 2 Gromov, Mikhael Leonidovich 2 Ivanov, Tjavdar 2 Ivrii, Victor Ja. 2 Jaye, Benjamin J. 2 Kamotski, Ilia V. 2 Kordyukov, Yuri A. 2 Koshelev, Aleksander I. 2 Natroshvili, David 2 Nikol’skiĭ, Sergeĭ Mikhaĭlovich 2 Otelbaev, Mukhtarbaj Otelbaevich 2 Plamenevskij, B. P. 2 Schwab, Christoph 2 Shargorodsky, Eugene 2 Stupyalis, Lyudvikas I. 2 Sunada, Toshikazu 2 Ziadé, Elia 1 Agranovsky, Mark L. 1 Alkhutov, Yuriy Alexandrovich 1 Alvino, Angelo 1 Barletta, Giuseppina 1 Ben-Artzi, Matania 1 Björn, Jana 1 Bukhshtaber, Viktor Matveevich 1 Bullough, Robin K. 1 Carbery, Anthony 1 Carlsson, Anders E. 1 Costea, Şerban 1 Costin, Ovidiu 1 Dikansky, Arnold 1 Dindoš, Martin 1 Duduchava, Roland 1 Egorov, Yuriĭ Vladimirovich 1 Elschner, Johannes 1 Fichera, Gaetano 1 Fomin, Alexey 1 Freidlin, Mark I. 1 Friedlander, L. F. 1 Friedlander, Leonid 1 Galloway, Greg 1 Gibiansky, E. 1 Hänler, Michael 1 Hansson, Kurt 1 Hellsten, Hans 1 Jin, Tianling ...and 39 more Co-Authors
all top 5

all top 5

#### Fields

 384 Partial differential equations (35-XX) 134 Functional analysis (46-XX) 109 Potential theory (31-XX) 77 Operator theory (47-XX) 44 Mechanics of deformable solids (74-XX) 42 Numerical analysis (65-XX) 41 Integral equations (45-XX) 35 Fluid mechanics (76-XX) 26 Real functions (26-XX) 26 Harmonic analysis on Euclidean spaces (42-XX) 22 Approximations and expansions (41-XX) 21 Functions of a complex variable (30-XX) 13 Global analysis, analysis on manifolds (58-XX) 12 Ordinary differential equations (34-XX) 10 History and biography (01-XX) 7 General and overarching topics; collections (00-XX) 7 Measure and integration (28-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 5 Quantum theory (81-XX) 3 Difference and functional equations (39-XX) 3 Integral transforms, operational calculus (44-XX) 3 Classical thermodynamics, heat transfer (80-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Dynamical systems and ergodic theory (37-XX) 1 Geometry (51-XX) 1 Differential geometry (53-XX) 1 Manifolds and cell complexes (57-XX) 1 Probability theory and stochastic processes (60-XX) 1 Statistics (62-XX)

#### Citations contained in zbMATH Open

412 Publications have been cited 4,054 times in 2,530 Documents Cited by Year
Sobolev spaces. Zbl 0727.46017
Maz’ya, V. G.
1985
Elliptic boundary value problems in domains with point singularities. Zbl 0947.35004
Kozlov, V. A.; Maz’ya, V. G.; Rossmann, J.
1997
Spectral problems associated with corner singularities of solutions to elliptic equations. Zbl 0965.35003
Kozlov, V. A.; Maz’ya, V. G.; Rossmann, J.
2001
On the Bourgain, Brezis, and Mironescu theorem concerning limiting embeddings of fractional Sobolev spaces. Zbl 1028.46050
Maz’ya, V.; Shaposhnikova, T.
2002
On the coefficients in the asymptotic of solutions of the elliptic boundary problem in domains with conical points. Zbl 0359.35024
Maz’ya, V. G.; Plamenevskij, B. A.
1977
Differentiable functions on bad domains. Zbl 0918.46033
Maz’ya, Vladimir G.; Poborchi, Sergei V.
1997
Sobolev spaces. With applications to elliptic partial differential equations. Transl. from the Russian by T. O. Shaposhnikova. 2nd revised and augmented ed. Zbl 1217.46002
2011
Global Lipschitz regularity for a class of quasilinear elliptic equations. Zbl 1220.35065
2011
Abschätzungen im $$L_p$$ und in Hölderschen Klassen und das Miranda- Agmonsche Maximumprinzip für die Lösungen elliptischer Randwertprobleme in Gebieten mit singulären Punkten auf dem Rande. Zbl 0371.35018
Maz’ya, V. G.; Plamenevskij, B. A.
1978
Asymptotic theory of elliptic boundary value problems in singularly perturbed domains. Vol. II. Transl. from the German by Boris Plamenevskii. Zbl 1127.35301
Maz’ya, V.; Nazarov, S.; Plamenevskii, B.
2000
Classes of domains and imbedding theorems for function spaces. Zbl 0114.31001
Maz’ya, V. G.
1960
Linear water waves. A mathematical approach. Zbl 0996.76001
Kuznetsov, N.; Maz’ya, V.; Vainberg, B.
2002
Elliptic equations in polyhedral domains. Zbl 1196.35005
2010
An iterative method for solving the Cauchy problem for elliptic equations. Zbl 0774.65069
Kozlov, V. A.; Maz’ya, V. G.; Fomin, A. V.
1991
Theory of multipliers in spaces of differentiable functions. Zbl 0645.46031
Maz’ya, V. G.; Shaposhnikova, T. O.
1985
Sobolev spaces. Transl. from the Russian by T. O. Shaposhnikova. Zbl 0692.46023
1985
Asymptotic analysis of fields in multi-structures. Zbl 0951.35004
Kozlov, V. A.; Maz’ya, V. G.; Movchan, A. B.
1999
Estimates in $$L_ p$$ and in Hölder classes and the Miranda-Agmon maximum principle for solutions of elliptic boundary value problems in domains with singular points on the boundary. Zbl 0554.35035
Maz’ya, V. G.; Plamenevskij, B. A.
1984
Global boundedness of the gradient for a class of nonlinear elliptic systems. Zbl 1298.35070
2014
Gradient regularity via rearrangements for $$p$$-Laplacian type elliptic boundary value problems. Zbl 1288.35128
2014
Critical Hardy–Sobolev inequalities. Zbl 1151.35368
Filippas, S.; Maz’ya, V.; Tertikas, A.
2007
$$L_p$$ estimates of solutions to mixed boundary value problems for the Stokes system in polyhedral domains. Zbl 1187.35157
Maz’ya, V.; Rossmann, J.
2007
Criteria of solvability for multidimensional Riccati equations. Zbl 1087.35513
Hansson, Kurt; Maz’ya, Vladimir G.; Verbitsky, Igor E.
1999
Pathological solutions to elliptic problems in divergence form with continuous coefficients. Zbl 1198.35055
Jin, Tianling; Maz’ya, Vladimir; Van Schaftingen, Jean
2009
Capacitary inequalities for fractional integrals, with applications to partial differential equations and Sobolev multipliers. Zbl 0834.31006
Maz’ya, Vladimir G.; Verbitsky, Igor E.
1995
The Schrödinger operator on the energy space: Boundedness and compactness criteria. Zbl 1013.35021
Maz’ya, Vladimir G.; Verbitsky, Igor E.
2002
On approximate approximations using Gaussian kernels. Zbl 0838.65005
1996
Über die Asymptotik der Lösungen elliptischer Randwertaufgaben in der Umgebung von Kanten. (On the asymptotic representation of solutions of elliptic boundary value problems in the neighbourhood of angles). Zbl 0672.35020
1988
The Dirichlet problem in Lipschitz domains for higher order elliptic systems with rough coefficients. Zbl 1199.35080
Maz’ya, Vladimir.; Mitrea, Marius; Shaposhnikova, Tatyana
2010
Lectures on isoperimetric and isocapacitary inequalities in the theory of Sobolev spaces. Zbl 1062.31009
2003
Weighted $$L_{p}$$ estimates of solutions to boundary value problems for second order elliptic systems in polyhedral domains. Zbl 1065.35109
2003
Approximate approximations from scattered data. Zbl 1119.41015
Lanzara, F.; Maz’ya, V.; Schmidt, G.
2007
On a question of Brezis and Marcus. Zbl 1121.26014
Filippas, S.; Maz’ya, V.; Tertikas, A.
2006
Zur Theorie des mehrdimensionalen Schrödinger-Operators. Zbl 0148.35602
Maz’ya, V. G.
1964
Sharp Hardy-Sobolev inequalities. Zbl 1058.26007
Filippas, S.; Maz’ya, V. G.; Tertikas, A.
2004
Non-linear potential theory. Zbl 0269.31004
Maz’ya, V. G.; Khavin, V. P.
1973
Green’s kernels and meso-scale approximations in perforated domains. Zbl 1273.35007
Maz’ya, Vladimir; Movchan, Alexander; Nieves, Michael
2013
Asymptotic expansions of the eigenvalues of boundary value problems for the Laplace operator in domains with small holes. Zbl 0566.35031
Maz’ya, V. G.; Nazarov, S. A.; Plamenevskij, B. A.
1985
Differential equations with operator coefficients with applications to boundary value problems for partial differential equations. Zbl 0920.35003
1999
On the coefficients in the asymptotics of solutions of elliptic boundary value problems in domains with conical points. Zbl 0554.35036
Maz’ya, V. G.; Plamenevskij, B. A.
1984
Asymptotic treatment of perforated domains without homogenization. Zbl 1185.35060
Maz’ya, V.; Movchan, A.
2010
The inhomogeneous Dirichlet problem for the Stokes system in Lipschitz domains with unit normal close to VMO. Zbl 1271.47072
Maz’ya, V.; Mitrea, M.; Shaposhnikova, T.
2009
Theory of Sobolev multipliers. With applications to differential and integral operators. Zbl 1157.46001
Maz’ya, Vladimir G.; Shaposhnikova, Tatyana O.
2009
Conductor and capacitary inequalities for functions on topological spaces and their applications to Sobolev-type imbeddings. Zbl 1105.46017
2005
On sign variation and the absence of “strong” zeros of solutions of elliptic equations. Zbl 0701.35062
Kozlov, V. A.; Kondrat’ev, V. A.; Maz’ya, V. G.
1990
Mixed boundary value problems for the stationary Navier-Stokes system in polyhedral domains. Zbl 1253.76019
Maz’ya, V.; Rossmann, J.
2009
Discreteness of spectrum and positivity criteria for Schrödinger operators. Zbl 1106.35043
2005
On the Agmon-Miranda maximum principle for solutions of elliptic equations in polyhedral and polygonal domains. Zbl 0753.35013
1991
On certain integral inequalities for functions of many variables. Zbl 0284.26011
Maz’ya, V. G.
1973
Well-posed elliptic Neumann problems involving irregular data and domains. Zbl 1200.35105
Alvino, Angelo; Cianchi, Andrea; Maz’ya, Vladimir G.; Mercaldo, Anna
2010
Criterion for the $$L^p$$-dissipativity of second order differential operators with complex coefficients. Zbl 1093.47047
Cialdea, A.; Maz’ya, V.
2005
Global gradient estimates in elliptic problems under minimal data and domain regularity. Zbl 1325.35027
2015
The Wiener test for higher order elliptic equations. Zbl 1129.35346
2002
On quasi-interpolation with non-uniformly distributed centers on domains and manifolds. Zbl 0976.41004
2001
Quasilinear elliptic problems with general growth and merely integrable, or measure, data. Zbl 1373.35113
2017
On the regularity of domains satisfying a uniform hour-glass condition and a sharp version of the Hopf-Oleinik boundary point principle. Zbl 1290.35046
2011
Boundedness of the gradient of a solution and Wiener test of order one for the biharmonic equation. Zbl 1166.35014
2009
Asymptotic formula for solutions to elliptic equations near the Lipschitz boundary. Zbl 1223.35144
2005
The form boundedness criterion for the relativistic Schrödinger operator. Zbl 1126.35011
2004
Schauder estimates for solutions to a mixed boundary value problem for the Stokes system in polyhedral domains. Zbl 1189.35085
Maz’ya, V. G.; Rossmann, J.
2006
Higher regularity in the layer potential theory for Lipschitz domains. Zbl 1132.31003
2005
The first boundary value problem for classical equations of mathematical physics in domains with partially smooth boundaries. I. Zbl 0532.35065
Maz’ya, V. G.; Plamenevskij, B. A.
1983
Existence and regularity of positive solutions of elliptic equations of Schrödinger type. Zbl 1307.35099
Jaye, B. J.; Maz’ya, V. G.; Verbitsky, I. E.
2012
Form boundedness of the general second-order differential operator. Zbl 1169.35014
Mazya, Vladimir G.; Verbitsky, Igor E.
2006
On pointwise interpolation inequalities for derivatives. Zbl 0936.26008
1999
Approximate approximations. Zbl 0827.65083
Maz’ya, V.
1994
On an iteration method for solving the Cauchy problem for elliptic equations. Zbl 0733.65056
Kozlov, V. A.; Maz’ya, V. G.; Fomin, A. V.
1991
Asymptotics of solutions to elliptic boundary value problems under singular perturbations of domains. Zbl 0462.35001
Maz’ya, V. G.; Nazarov, S. A.; Plamenevskiĭ, B. A.
1981
Second-order two-sided estimates in nonlinear elliptic problems. Zbl 1398.35078
2018
Estimates for differential operators of vecor analysis involving $$L^{1}$$-norm. Zbl 1187.42011
2010
An elementary proof of the Brezis and Mironescu theorem on the composition operator in fractional Sobolev spaces. Zbl 1006.46024
Maz’ya, V.; Shaposhnikova, T.
2002
Spectral properties of the operator bundles generated by elliptic boundary-value problems in a cone. Zbl 0672.35050
Kozlov, V. A.; Maz’ya, V. G.
1988
Multipliers in spaces of differentiable functions. Zbl 0695.46016
Maz’ya, V. G.; Shaposhnikova, T. O.
1986
Über ein entartetes Problem mit schiefer Ableitung. Zbl 0262.35024
Maz’ya, V. G.
1972
Asymptotic behavior of solutions of elliptic equations of the second order close to a boundary. I. Zbl 0243.35025
Verzhbinskii, G. M.; Maz’ya, V. G.
1972
On continuity in a boundary point of solutions of quasilinear elliptic equations. Zbl 0252.35024
Maz’ya, V. G.
1970
Examples of nonregular solutions of quasilinear elliptic equations with analytic coefficients. Zbl 0179.43601
Maz’ya, V. G.
1968
Neumann problems and isocapacitary inequalities. Zbl 1146.35041
2008
Einbettungssätze für Sobolewsche Räume. Teil 1. Übers. aus dem Russischen von Jürgen Nagel. Zbl 0429.46018
1979
Coefficients in the asymptotics of the solutions of elliptic boundary- value problems in a cone. Zbl 0396.35038
Maz’ya, V. G.; Plamenevskij, B. A.
1978
On weak solutions of the Dirichlet and Neumann problems. Zbl 0226.35027
Maz’ya, V. G.
1971
Potential theory and function theory for irregular regions. Zbl 0177.37502
Burago, Yu. D.; Maz’ya, V. G.
1969
Quasilinear elliptic equations and weighted Sobolev-Poincaré inequalities with distributional weights. Zbl 1331.35148
Jaye, Benjamin J.; Maz’ya, Vladimir G.; Verbitsky, Igor E.
2013
Mesoscale asymptotic approximations to solutions of mixed boundary value problems in perforated domains. Zbl 1223.35293
Maz’ya, V.; Movchan, A.; Nieves, M.
2011
On the fast computation of high dimensional volume potentials. Zbl 1213.65046
Lanzara, Flavia; Maz’ya, Vladimir; Schmidt, Gunther
2011
Pointwise estimates for Green’s kernel of a mixed boundary value problem to the Stokes system in a polyhedral cone. Zbl 1161.35465
Maz’ya, V.; Rossmann, J.
2005
Discreteness of spectrum and strict positivity criteria for magnetic Schrödinger operators. Zbl 1140.35300
2004
“Approximate approximations” and the cubature of potentials. Zbl 0845.65008
1995
On iterative procedures for solving ill-posed boundary value problems that preserve differential equations. Zbl 0732.65090
Kozlov, V. A.; Maz’ya, V. G.
1990
The three-dimensional problem of steady-state motion of a fluid with a free surface. Zbl 0553.76028
Maz’ya, V. G.; Plamenevskiĭ, B. A.; Stupelis, L. I.
1984
Certain questions of potential theory and function theory for regions with irregular boundaries. Zbl 0172.14903
Burago, Yu. D.; Maz’ya, V. G.
1967
Can one see the fundamental frequency of a drum? Zbl 1099.35071
2005
Asymptotic representation of elastic fields in a multi-structure. Zbl 0846.73009
Kozlov, V. A.; Maz’ya, V. G.; Movchan, A. B.
1995
On stress singularities near the boundary of a polygonal crack. Zbl 0728.73057
Kozlov, V. A.; Maz’ya, V. G.
1991
Asymptotics of energy integrals under small perturbations of the boundary close to angular and conic points. Zbl 0668.35027
Maz’ya, V. G.; Nazarov, S. A.
1987
The first boundary value problem for classical equations of mathematical physics in domains with piecewise smooth boundaries. II. Zbl 0554.35099
Maz’ya, V. G.; Plamenevskij, B. A.
1983
$$L_ p-$$estimates of solutions of elliptic boundary value problems in domains with edges. Zbl 0453.35025
Mazya, V. G.; Plamenevskij, B. A.
1980
Fast cubature of volume potentials over rectangular domains by approximate approximations. Zbl 1294.65034
Lanzara, F.; Maz’ya, V.; Schmidt, G.
2014
Sharp real-part theorems in the upper halfplane and similar estimates for harmonic functions. Zbl 1291.30150
Kresin, G.; Maz’ya, V.
2011
Sharp pointwise estimates for directional derivatives of harmonic functions in a multidimensional ball. Zbl 1222.31003
Kresin, G.; Maz’ya, V.
2010
Second-order regularity for parabolic $$p$$-Laplace problems. Zbl 1439.35204
2020
Approximation of solutions to nonstationary Stokes system. Zbl 1435.65160
Lanzara, F.; Maz’ya, V.; Schmidt, G.
2020
Optimal second-order regularity for the $$p$$-Laplace system. Zbl 1437.35404
2019
Accretivity of the general second order linear differential operator. Zbl 1422.35029
Maz’ya, V. G.; Verbitsky, I. E.
2019
Fast cubature of high dimensional biharmonic potential based on approximate approximations. Zbl 07144083
Lanzara, Flavia; Maz’ya, Vladimir; Schmidt, Gunther
2019
The $$L^p$$-dissipativity of certain differential and integral operators. Zbl 1447.47035
2019
A fast solution method for time dependent multidimensional Schrödinger equations. Zbl 1453.65054
Lanzara, F.; Maz’ya, V.; Schmidt, G.
2019
Second-order two-sided estimates in nonlinear elliptic problems. Zbl 1398.35078
2018
Meso-scale approximations of fields around clusters of defects. Zbl 1403.35080
Maz’ya, Vladimir G.; Movchan, A. B.
2018
Seventy five (thousand) unsolved problems in analysis and partial differential equations. Zbl 1398.35019
2018
The $$L^p$$-dissipativity of first order partial differential operators. Zbl 1394.35133
Cialdea, A.; Maz’ya, V.
2018
Accurate computation of the high dimensional diffraction potential over hyper-rectangles. Zbl 07121691
Lanzara, Flavia; Maz’ya, Vladimir; Schmidt, Gunther
2018
On eigenfunctions of the Fourier transform. Zbl 1408.42003
Lanzara, F.; Maz’ya, V.
2018
Boundary behavior of solutions to elliptic equations in general domains. Zbl 1409.35073
2018
Polyharmonic capacity and Wiener test of higher order. Zbl 1411.35056
2018
Quasilinear elliptic problems with general growth and merely integrable, or measure, data. Zbl 1373.35113
2017
Note on a nonstandard eigenfunction of the planar Fourier transform. Zbl 1386.46039
Lanzara, F.; Maz’ya, V.
2017
Quasilinear elliptic equations on noncompact Riemannian manifolds. Zbl 1382.35110
Barletta, Giuseppina; Cianchi, Andrea; Maz’ya, Vladimir
2017
Mesoscale models and approximate solutions for solids containing clouds of voids. Zbl 1381.35176
Maz’ya, V. G.; Movchan, A. B.; Nieves, M. J.
2016
Approximation of solutions to multidimensional parabolic equations by approximate approximations. Zbl 1348.65061
Lanzara, F.; Maz’ya, V.; Schmidt, G.
2016
Sobolev inequalities in arbitrary domains. Zbl 1346.46022
2016
Global gradient estimates in elliptic problems under minimal data and domain regularity. Zbl 1325.35027
2015
Criteria for invariance of convex sets for linear parabolic systems. Zbl 1346.35093
2015
Pointwise inequalities for elliptic boundary value problems. Zbl 1333.35046
Luo, G.; Maz’ya, V. G.
2015
Global boundedness of the gradient for a class of nonlinear elliptic systems. Zbl 1298.35070
2014
Gradient regularity via rearrangements for $$p$$-Laplacian type elliptic boundary value problems. Zbl 1288.35128
2014
Fast cubature of volume potentials over rectangular domains by approximate approximations. Zbl 1294.65034
Lanzara, F.; Maz’ya, V.; Schmidt, G.
2014
Regularity of solutions to the polyharmonic equation in general domains. Zbl 1292.35114
2014
Semi-bounded differential operators, contractive semigroups and beyond. Zbl 1317.47002
2014
Mesoscale approximations for solutions of the Dirichlet problem in a perforated elastic body. Zbl 1311.74021
Maz’ya, V. G.; Movchan, A. B.; Nieves, M. J.
2014
Optimal pointwise stimates for derivatives of solutions to Laplace, Lamé, and Stokes equations. Zbl 1302.31008
Kresin, G.; Maz’ya, V. G.
2014
The integrability of negative powers of the solution to the Saint Venant problem. Zbl 1297.35088
Carbery, Anthony; Maz’ya, Vladimir; Mitrea, Marius; Rule, David J.
2014
$$L^{1,p}$$-coercitivity and estimates of the Green function of the Neumann problem in a convex domain. Zbl 1302.35146
Alkhutov, Yu.; Maz’ya, V. G.
2014
Notes on Hölder regularity of a boundary point with respect to an elliptic operator of second order. Zbl 1304.35174
Maz’ya, V. G.
2014
Green’s kernels and meso-scale approximations in perforated domains. Zbl 1273.35007
Maz’ya, Vladimir; Movchan, Alexander; Nieves, Michael
2013
Quasilinear elliptic equations and weighted Sobolev-Poincaré inequalities with distributional weights. Zbl 1331.35148
Jaye, Benjamin J.; Maz’ya, Vladimir G.; Verbitsky, Igor E.
2013
Solvability of a boundary integral equation on a polyhedron. Zbl 1273.35087
Grachev, N. V.; Maz’ya, V. G.
2013
Bounds for eigenfunctions of the Laplacian on noncompact Riemannian manifolds. Zbl 1280.58018
2013
$$L^p$$-dissipativity of the Lamé operator. Zbl 1307.74017
Cialdea, A.; Maz’ya, V.
2013
Computation of volume potentials over bounded domains via approximate approximations. Zbl 1273.65040
Lanzara, F.; Maz’ya, V. G.; Schmidt, G.
2013
Estimate for a solution to the water wave problem in the presence of a submerged body. Zbl 1311.76014
Kamotski, I.; Mazýa, V.
2013
Solvability of boundary singular integral operators of elasticity on surfaces with conic points. Zbl 1273.35086
Grachev, N. V.; Maz’ya, V. G.
2013
Existence and regularity of positive solutions of elliptic equations of Schrödinger type. Zbl 1307.35099
Jaye, B. J.; Maz’ya, V. G.; Verbitsky, I. E.
2012
Invertibility of boundary integral operators of elasticity on surfaces with conic points. Zbl 1381.45016
Grachev, N. V.; Maz’ya, V. G.
2012
Maximum principles and sharp constants for solutions of elliptic and parabolic systems. Zbl 1255.35001
2012
Sharp real-part theorems for high order derivatives. Zbl 1277.30016
Kresin, G.; Maz’ya, V.
2012
Estimates for kernels of inverse operators of integral equations of elasticity on surfaces with conic points. Zbl 1381.45039
Grachev, N. V.; Maz’ya, V. G.
2012
Uniform asymptotics of Green’s kernels in perforated domains and meso-scale approximations. Zbl 1234.35264
Maz’ya, V.; Movchan, A.
2012
On the linear water wave problem in the presence of a critically submerged body. Zbl 06138497
Kamotski, I. V.; Maz’ya, V. G.
2012
Boundedness of solutions to the Schrödinger equation under Neumann boundary conditions. Zbl 1259.35072
2012
Representations and estimates for inverse operators in the harmonic potential theory for polyhedra. Zbl 1252.35128
2012
Sobolev spaces. With applications to elliptic partial differential equations. Transl. from the Russian by T. O. Shaposhnikova. 2nd revised and augmented ed. Zbl 1217.46002
2011
Global Lipschitz regularity for a class of quasilinear elliptic equations. Zbl 1220.35065
2011
On the regularity of domains satisfying a uniform hour-glass condition and a sharp version of the Hopf-Oleinik boundary point principle. Zbl 1290.35046
2011
Mesoscale asymptotic approximations to solutions of mixed boundary value problems in perforated domains. Zbl 1223.35293
Maz’ya, V.; Movchan, A.; Nieves, M.
2011
On the fast computation of high dimensional volume potentials. Zbl 1213.65046
Lanzara, Flavia; Maz’ya, Vladimir; Schmidt, Gunther
2011
Sharp real-part theorems in the upper halfplane and similar estimates for harmonic functions. Zbl 1291.30150
Kresin, G.; Maz’ya, V.
2011
Differentiability of solutions to second-order elliptic equations via dynamical systems. Zbl 1225.35070
2011
Accurate cubature of volume potentials over high-dimensional half-spaces. Zbl 1223.65017
Lanzara, F.; Maz’ya, V. G.; Schmidt, G.
2011
On the third boundary value problem in domains with cusps. Zbl 1282.35148
Kamotski, I. V.; Maz’ya, V. G.
2011
Brezis-Gallouet-Wainger type inequality for irregular domains. Zbl 1232.46034
2011
On the discreteness of the spectrum of the Laplacian on noncompact Riemannian manifolds. Zbl 1269.58011
2011
Boundary characteristic point regularity for semilinear reaction-diffusion equations: towards an ODE criterion. Zbl 1286.35123
Galaktionov, V. A.; Maz’ya, V.
2011
Recent progress in elliptic equations and systems of arbitrary order with rough coefficients in Lipschitz domains. Zbl 1263.35097
2011
Existence and uniqueness of an energy solution to the Dirichlet problem for the Laplace equation in the exterior of a multi-dimensional paraboloid. Zbl 1219.35073
Maz’ya, V.; Poborchi, S.
2011
Elliptic equations in polyhedral domains. Zbl 1196.35005
2010
The Dirichlet problem in Lipschitz domains for higher order elliptic systems with rough coefficients. Zbl 1199.35080
Maz’ya, Vladimir.; Mitrea, Marius; Shaposhnikova, Tatyana
2010
Asymptotic treatment of perforated domains without homogenization. Zbl 1185.35060
Maz’ya, V.; Movchan, A.
2010
Well-posed elliptic Neumann problems involving irregular data and domains. Zbl 1200.35105
Alvino, Angelo; Cianchi, Andrea; Maz’ya, Vladimir G.; Mercaldo, Anna
2010
Estimates for differential operators of vecor analysis involving $$L^{1}$$-norm. Zbl 1187.42011
2010
Sharp pointwise estimates for directional derivatives of harmonic functions in a multidimensional ball. Zbl 1222.31003
Kresin, G.; Maz’ya, V.
2010
Optimal estimates for the gradient of harmonic functions in the multidimensional half-space. Zbl 1221.35111
2010
Green’s kernels for transmission problems in bodies with small inclusions. Zbl 1223.35123
Maz’ya, V.; Movchan, A.; Nieves, M.
2010
$$L^p$$ solvability of the stationary Stokes problem in domains with conical singularity in any dimension. Zbl 1298.35049
Dindoš, M.; Maz’ya, V.
2010
On solvability of boundary integral equations of potential theory for a multidimensional cusp domain. Zbl 1402.35102
Maz’ya, V.; Poborchi, S.
2010
On the fundamental solution of an elliptic equation in nondivergence form. Zbl 1213.35022
2010
Wiener type regularity of a boundary point for the 3D Lamé system. Zbl 1185.35281
2010
Boundary integral equations on contours with peaks. Transl. into English and edited by Tatyana Shaposhnikova. Zbl 1179.45001
Maz’ya, Vladimir G.; Soloviev, Alexander A.
2010
Pathological solutions to elliptic problems in divergence form with continuous coefficients. Zbl 1198.35055
Jin, Tianling; Maz’ya, Vladimir; Van Schaftingen, Jean
2009
The inhomogeneous Dirichlet problem for the Stokes system in Lipschitz domains with unit normal close to VMO. Zbl 1271.47072
Maz’ya, V.; Mitrea, M.; Shaposhnikova, T.
2009
Theory of Sobolev multipliers. With applications to differential and integral operators. Zbl 1157.46001
Maz’ya, Vladimir G.; Shaposhnikova, Tatyana O.
2009
Mixed boundary value problems for the stationary Navier-Stokes system in polyhedral domains. Zbl 1253.76019
Maz’ya, V.; Rossmann, J.
2009
Boundedness of the gradient of a solution and Wiener test of order one for the biharmonic equation. Zbl 1166.35014
2009
On the boundedness of first derivatives for solutions to the Neumann-Laplace problem in a convex domain. Zbl 1205.35069
2009
A collection of sharp dilation invariant integral inequalities for differentiable functions. Zbl 1161.26302
2009
Boundedness of the gradient of a solution to the Neumann-Laplace problem in a convex domain. Zbl 1167.35013
2009
Conductor inequalities and criteria for Sobolev-Lorentz two-weight inequalities. Zbl 1165.26009
2009
Pointwise estimates for the polyharmonic Green function in general domains. Zbl 1193.35032
2009
Uniform asymptotics of Green’s kernels for mixed and Neumann problems in domains with small holes and inclusions. Zbl 1171.35027
2009
Gauge optimization and spectral properties of magnetic Schrödinger operators. Zbl 1185.35044
2009
Unique solvability of the integral equation for harmonic simple layer potential on the boundary of a domain with a peak. Zbl 1186.31004
Maz’ya, V. G.; Poborchii, S. V.
2009
A maximum modulus estimate for solutions of the Navier-Stokes system in domains of polyhedral type. Zbl 1170.35077
Maz’ya, V.; Rossmann, J.
2009
Uniqueness of the solution to an inverse thermoelasticity problem. Zbl 1224.74030
Kozlov, V. A.; Maz’ya, V. G.; Fomin, A. V.
2009
On representation of the solution of the Neumann problem in a domain with peak by the harmonic simple layer potential. Zbl 1179.35109
Maz’ya, V. G.; Poborchii, S. V.
2009
Integral and isocapacitary inequalities. Zbl 1190.26010
2009
Neumann problems and isocapacitary inequalities. Zbl 1146.35041
2008
Sharp Hardy-Leray inequality for axisymmetric divergence-free fields. Zbl 1147.35122
Costin, O.; Maz’ya, V.
2008
Uniform asymptotic approximations of Green’s functions in a long rod. Zbl 1157.35303
Maz’ya, V.; Movchan, A.
2008
Boundedness of the Hessian of a biharmonic function in a convex domain. Zbl 1186.35051
2008
Approximate Hermite quasi-interpolation. Zbl 1151.41307
Lanzara, F.; Maz’ya, V.; Schmidt, G.
2008
...and 312 more Documents
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#### Cited by 2,518 Authors

 141 Nazarov, Sergeĭ Aleksandrovich 135 Maz’ya, Vladimir Gilelevich 38 Cianchi, Andrea 32 Kozlov, Vladimir A. 28 Nicaise, Serge 25 Medková, Dagmar 23 Mingione, Giuseppe 21 Verbitsky, Igor E. 21 Xiao, Jie 20 Mitrea, Marius 19 Schmidt, Gunther 18 Dauge, Monique 18 Khludnev, Aleksandr Mikhaĭlovich 17 Kresin, Gershon I. 16 Kuusi, Tuomo 16 Lanzara, Flavia 16 Movchan, Alexander B. 15 Rehberg, Joachim 15 Rossmann, Jürgen 15 Tertikas, Achilles 15 Wendland, Wolfgang L. 14 Mitrea, Irina 14 Musolino, Paolo 14 Pick, Luboš 14 Pileckas, Konstantin 14 Salimov, Ruslan Radikovich 14 Taskinen, Jari 13 Filippas, Stathis 13 Kuznetsov, Nikolai Germanovich 13 Li, Hengguang 13 Mayboroda, Svitlana 13 Nistor, Victor 13 Valdinoci, Enrico 12 Sändig, Anna-Margarete 11 Argatov, Ivan I. 11 Boyd, John Philip 11 Kweon, Jae Ryong 11 Vodop’yanov, Sergeĭ Konstantinovich 10 Abdellaoui, Boumediene 10 Beneš, Michal 10 Byun, Sun-Sig 10 Costabel, Martin 10 Lanza de Cristoforis, Massimo 10 Lesnic, Daniel 10 Marin, Liviu 10 Milman, Mario Marcos 10 Nguyen Cong Phuc 10 Plamenevskiĭ, Boris Alekseevich 10 Stepanov, Vladimir Dmitrievich 10 Yao, Fengping 9 Dalla Riva, Matteo 9 Dipierro, Serena 9 Fiscella, Alessio 9 Haller-Dintelmann, Robert 9 Lu, Guozhen 9 Mercaldo, Anna 9 Motygin, Oleg Valer’evich 9 Nasibullin, Ramil Gaisa’evich 9 Nguyen Manh Hung 9 Ortega, Joaquin Ma. 9 Panasenko, Grigory P. 9 Pucci, Patrizia 9 Sini, Mourad 9 Solonnikov, Vsevolod Alekseevich 9 Spector, Daniel E. 9 Tarkhanov, Nikolai N. 9 Vähäkangas, Antti V. 8 Apel, Thomas 8 Avkhadiev, Farit Gabidinovich 8 Brasco, Lorenzo 8 Brenner, Susanne Cecelia 8 Cascante, Carme 8 Chechkin, Gregory Aleksandrovich 8 Gala, Sadek 8 Kohr, Mirela 8 Koskela, Pekka 8 Lubuma, Jean Mbaro-Saman 8 Shvartsman, Pavel 8 Sickel, Winfried 8 Squassina, Marco 8 Sweers, Guido H. 8 Ushakova, Elena Pavlovna 7 Borisov, Denis Ivanovich 7 Bousquet, Pierre 7 Chlebicka, Iwona 7 Dahlke, Stephan 7 Diening, Lars 7 Dong, Hongjie 7 Elliott, Lionel 7 Gol’dshtein, Vladimir Mikhailovich 7 Hamamoto, Naoki 7 Hurri-Syrjānen, Ritva 7 Ingham, Derek Binns 7 Kaiser, Hans-Christoph 7 Lemarié-Rieusset, Pierre Gilles 7 Martín, Joaquim 7 Mitrea, Dorina 7 Peral Alonso, Ireneo 7 Pierotti, Dario 7 Ponce, Augusto C. ...and 2,418 more Authors
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#### Cited in 334 Serials

 127 Journal of Mathematical Analysis and Applications 119 Journal of Functional Analysis 111 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 102 Journal of Mathematical Sciences (New York) 97 Journal of Differential Equations 51 Calculus of Variations and Partial Differential Equations 44 Journal de Mathématiques Pures et Appliquées. Neuvième Série 42 Advances in Mathematics 40 Journal of Computational and Applied Mathematics 36 Mathematical Methods in the Applied Sciences 36 Mathematische Nachrichten 36 Transactions of the American Mathematical Society 34 Siberian Mathematical Journal 30 Proceedings of the American Mathematical Society 29 Archive for Rational Mechanics and Analysis 29 Mathematical Notes 29 Comptes Rendus. Mathématique. Académie des Sciences, Paris 27 Potential Analysis 24 Computer Methods in Applied Mechanics and Engineering 24 Mathematics of Computation 24 Annali di Matematica Pura ed Applicata. Serie Quarta 23 Journal of Applied Mathematics and Mechanics 23 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 23 St. Petersburg Mathematical Journal 22 Mathematische Annalen 22 Numerische Mathematik 22 Communications in Partial Differential Equations 20 ZAMP. Zeitschrift für angewandte Mathematik und Physik 19 Applicable Analysis 19 Computers & Mathematics with Applications 19 Zeitschrift für Analysis und ihre Anwendungen 19 The Journal of Geometric Analysis 18 Journal of Computational Physics 17 Annales de l’Institut Fourier 17 Discrete and Continuous Dynamical Systems 16 Journal d’Analyse Mathématique 16 Applied Mathematics and Computation 16 Communications on Pure and Applied Analysis 15 Integral Equations and Operator Theory 15 Engineering Analysis with Boundary Elements 15 Complex Variables and Elliptic Equations 14 Journal of Fluid Mechanics 14 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 13 Doklady Mathematics 13 Lobachevskii Journal of Mathematics 13 Discrete and Continuous Dynamical Systems. Series S 12 Wave Motion 12 Prikladnaya Matematika i Mekhanika 12 Czechoslovak Mathematical Journal 12 Functional Analysis and its Applications 12 Nonlinear Analysis. Real World Applications 12 Complex Analysis and Operator Theory 11 Communications in Mathematical Physics 11 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 11 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 11 Journal of Mathematical Fluid Mechanics 11 Journal of the European Mathematical Society (JEMS) 11 Boundary Value Problems 10 Ukrainian Mathematical Journal 10 Arkiv för Matematik 10 Applied Numerical Mathematics 10 Applications of Mathematics 10 SIAM Journal on Mathematical Analysis 10 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 10 Multiscale Modeling & Simulation 9 Journal of Soviet Mathematics 9 Mathematische Zeitschrift 9 Bulletin des Sciences Mathématiques 9 Abstract and Applied Analysis 9 Communications in Contemporary Mathematics 9 Differential Equations 9 Proceedings of the Steklov Institute of Mathematics 8 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 8 Journal of Approximation Theory 8 Mathematika 8 Numerical Functional Analysis and Optimization 8 Numerical Algorithms 8 NoDEA. Nonlinear Differential Equations and Applications 8 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 8 Acta Mathematica Sinica. English Series 8 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 8 Journal of Fixed Point Theory and Applications 7 Archiv der Mathematik 7 Manuscripta Mathematica 7 SIAM Journal on Numerical Analysis 7 RAIRO. Modélisation Mathématique et Analyse Numérique 7 Journal of Scientific Computing 7 Computational Mathematics and Mathematical Physics 7 Applied Mathematical Modelling 7 Russian Journal of Mathematical Physics 7 Sbornik: Mathematics 7 Advanced Nonlinear Studies 7 Computational Methods and Function Theory 7 Analysis and Applications (Singapore) 7 Ufimskiĭ Matematicheskiĭ Zhurnal 7 Eurasian Mathematical Journal 6 Journal of Mathematical Physics 6 Lithuanian Mathematical Journal 6 Applied Mathematics and Optimization 6 Monatshefte für Mathematik ...and 234 more Serials
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#### Cited in 54 Fields

 1,593 Partial differential equations (35-XX) 462 Functional analysis (46-XX) 324 Numerical analysis (65-XX) 280 Mechanics of deformable solids (74-XX) 280 Fluid mechanics (76-XX) 235 Operator theory (47-XX) 212 Potential theory (31-XX) 209 Real functions (26-XX) 157 Calculus of variations and optimal control; optimization (49-XX) 124 Harmonic analysis on Euclidean spaces (42-XX) 100 Functions of a complex variable (30-XX) 99 Global analysis, analysis on manifolds (58-XX) 82 Integral equations (45-XX) 58 Approximations and expansions (41-XX) 51 Differential geometry (53-XX) 51 Optics, electromagnetic theory (78-XX) 43 Quantum theory (81-XX) 40 Ordinary differential equations (34-XX) 37 Probability theory and stochastic processes (60-XX) 33 Measure and integration (28-XX) 23 Statistical mechanics, structure of matter (82-XX) 20 Convex and discrete geometry (52-XX) 20 Classical thermodynamics, heat transfer (80-XX) 19 Several complex variables and analytic spaces (32-XX) 19 Systems theory; control (93-XX) 18 Biology and other natural sciences (92-XX) 13 Dynamical systems and ergodic theory (37-XX) 11 Difference and functional equations (39-XX) 10 Abstract harmonic analysis (43-XX) 10 Geophysics (86-XX) 9 History and biography (01-XX) 8 Special functions (33-XX) 7 Manifolds and cell complexes (57-XX) 5 Combinatorics (05-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 5 Integral transforms, operational calculus (44-XX) 4 Number theory (11-XX) 4 Mechanics of particles and systems (70-XX) 3 Topological groups, Lie groups (22-XX) 3 General topology (54-XX) 3 Computer science (68-XX) 3 Relativity and gravitational theory (83-XX) 2 General and overarching topics; collections (00-XX) 2 Group theory and generalizations (20-XX) 2 Geometry (51-XX) 2 Statistics (62-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Mathematical logic and foundations (03-XX) 1 Algebraic geometry (14-XX) 1 $$K$$-theory (19-XX) 1 Astronomy and astrophysics (85-XX) 1 Operations research, mathematical programming (90-XX) 1 Information and communication theory, circuits (94-XX) 1 Mathematics education (97-XX)

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