Edit Profile (opens in new tab) Martio, Olli Compute Distance To: Compute Author ID: martio.olli Published as: Martio, O.; Martio, Olli Homepage: https://researchportal.helsinki.fi/en/persons/olli-martio External Links: MGP · Wikidata · ResearchGate · Math-Net.Ru · IdRef Documents Indexed: 186 Publications since 1967, including 7 Books 9 Contributions as Editor Reviewing Activity: 322 Reviews Biographic References: 3 Publications Co-Authors: 70 Co-Authors with 148 Joint Publications 1,834 Co-Co-Authors all top 5 Co-Authors 47 single-authored 40 Vuorinen, Matti Keijo Kustaa 24 Gutlyanskiĭ, Vladimir Ya. 23 Ryazanov, Vladimir Il’ich 17 Miklyukov, Vladimir Mikhaiĭlovich 14 Srebro, Uri 9 Dovgoshey, Oleksiy Alfredovich 9 Kinnunen, Juha 8 Kilpeläinen, Tero 8 Li, Gongbao 8 Väisälä, Jussi 7 Heinonen, Juha 6 Lindqvist, Peter 5 Gehring, Frederick William 5 Malý, Jan 5 Rickman, Seppo Uolevi 5 Yakubov, Eduard H. 4 Granlund, Seppo 4 Honzlová Exnerová, Vendula 4 Koskela, Pekka 4 Ławrynowicz, Julian Mieczysław 3 Bojarski, Bogdan 3 Laine, Ilpo 3 Näkki, Raimo 2 Hag, Kari 2 Sarvas, Jukka 2 Sugawa, Toshiyuki 1 Atiyah, Michael Francis 1 Avkhadiev, Farit Gabidinovich 1 Bishop, Christopher James 1 Björn, Anders 1 Botvinnik, V. A. 1 Chirka, Evgeni M. 1 Dubinin, Vladimir N. 1 Fernández Pérez, José Luis 1 Franke, Dirk Christoph 1 Fuchs, Martin 1 Gol’dstein, Vladimir Mikailovitch 1 Goryainov, Viktor V. 1 Grigor’yan, Alexander Asaturovich 1 Hag, Per 1 Hajłasz, Piotr 1 Harjulehto, Petteri 1 Hästö, Peter A. 1 Kalenda, Ondřej F. K. 1 Kallunki, Sari 1 Kesel’man, V. M. 1 Klyachin, Vladimir Aleksandrovich 1 Latfullin, T. G. 1 Loboda, Alexander Vasil’evich 1 Marola, Niko 1 Nirenberg, Louis 1 Øksendal, Bernt Karsten 1 Pelikh, V. I. 1 Pinchuk, Sergey 1 Ponnusamy, Saminathan 1 Porru, Giovanni 1 Reshetnyak, Yuriĭ Grigor’evich 1 Romanov, Aleksandr Sergeevich 1 Rzazanov, V. 1 Saksman, Eero 1 Sbordone, Carlo 1 Sergeev, Armen Glebovich 1 Tarazov, Promarz M. 1 Tkachev, Vladimir G. 1 Vodop’yanov, Sergeĭ Konstantinovich 1 Wisk, R. 1 Zając, Józef 1 Zhuravlëv, I. V. 1 Ziemer, William Paul 1 Zorich, Vladimir Antonovich all top 5 Serials 12 Annales Academiae Scientiarum Fennicae. Series A I. Mathematica 10 Doklady Mathematics 9 Annales Academiae Scientiarum Fennicae. Series A I 7 Journal d’Analyse Mathématique 6 Revue Roumaine de Mathématiques Pures et Appliquées 6 Annales Academiae Scientiarum Fennicae. Mathematica 5 Arkhimedes 5 Complex Variables. Theory and Application 4 Indiana University Mathematics Journal 4 Mathematica Scandinavica 4 Results in Mathematics 4 Dopovidi Natsional’noï Akademiï Nauk Ukraïny. Matematyka, Pryrodoznavstvo, Tekhnichni Nauky 4 Bericht. Universität Jyväskylä. Mathematisches Institut 3 Arkiv för Matematik 3 Bulletin of the London Mathematical Society 3 Proceedings of the American Mathematical Society 2 Journal of Mathematical Analysis and Applications 2 Acta Mathematica 2 Collectanea Mathematica 2 Journal of Functional Analysis 2 Manuscripta Mathematica 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Pacific Journal of Mathematics 2 Transactions of the American Mathematical Society 2 Siberian Advances in Mathematics 2 Expositiones Mathematicae 2 Journal of Mathematical Sciences (New York) 2 Izvestiya: Mathematics 2 Conformal Geometry and Dynamics 2 Computational Methods and Function Theory 2 Ukraïns’kyĭ Matematychnyĭ Visnyk 1 Houston Journal of Mathematics 1 Israel Journal of Mathematics 1 Russian Mathematical Surveys 1 Studia Mathematica 1 Beiträge zur Algebra und Geometrie 1 Annales de l’Institut Fourier 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Annales Universitatis Mariae Curie-Skłodowska. Sectio A. Mathematica 1 Czechoslovak Mathematical Journal 1 Duke Mathematical Journal 1 Functiones et Approximatio. Commentarii Mathematici 1 Illinois Journal of Mathematics 1 International Journal of Mathematics and Mathematical Sciences 1 Journal of the London Mathematical Society. Second Series 1 Journal für die Reine und Angewandte Mathematik 1 Mathematische Annalen 1 Mathematische Nachrichten 1 Michigan Mathematical Journal 1 Nagoya Mathematical Journal 1 Ricerche di Matematica 1 Siberian Mathematical Journal 1 Tôhoku Mathematical Journal. Second Series 1 Forum Mathematicum 1 European Journal of Applied Mathematics 1 The Journal of Geometric Analysis 1 Communications in Partial Differential Equations 1 Potential Analysis 1 Mathematical Research Letters 1 Bulletin de la Société des Sciences et des Lettres de Łódź. Série: Recherches sur les Déformations 1 Abstract and Applied Analysis 1 Journal of Inequalities and Applications 1 Annals of Combinatorics 1 Trudy Instituta Prikladnoĭ Matematiki i Mekhaniki 1 Advanced Nonlinear Studies 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Boundary Value Problems 1 Bulletin of the American Mathematical Society 1 Pure and Applied Mathematics Quarterly 1 Banach Center Publications 1 Textos de Matemática. Série B 1 Journal of Fixed Point Theory and Applications 1 Complex Analysis and Operator Theory 1 Zbirnyk Prats’ Instytutu Matematyky NAN Ukraïny 1 EMS Tracts in Mathematics 1 Advances in Calculus of Variations 1 Nonlinear Analysis. Theory, Methods & Applications 1 Oxford Mathematical Monographs 1 Dover Books on Mathematics all top 5 Fields 112 Functions of a complex variable (30-XX) 46 Potential theory (31-XX) 45 Partial differential equations (35-XX) 17 Functional analysis (46-XX) 10 Real functions (26-XX) 10 Measure and integration (28-XX) 9 General and overarching topics; collections (00-XX) 9 General topology (54-XX) 8 Calculus of variations and optimal control; optimization (49-XX) 6 History and biography (01-XX) 6 Global analysis, analysis on manifolds (58-XX) 5 Manifolds and cell complexes (57-XX) 4 Several complex variables and analytic spaces (32-XX) 4 Differential geometry (53-XX) 3 Group theory and generalizations (20-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 2 Number theory (11-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Algebraic topology (55-XX) 1 Combinatorics (05-XX) 1 Ordinary differential equations (34-XX) 1 Mechanics of deformable solids (74-XX) 1 Fluid mechanics (76-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 134 Publications have been cited 2,986 times in 1,881 Documents Cited by ▼ Year ▼ Nonlinear potential theory of degenerate elliptic equations. Zbl 0780.31001Heinonen, Juha; Kilpeläinen, Tero; Martio, Olli 598 1993 Nonlinear potential theory of degenerate elliptic equations. Unabridged republication of the 1993 original. Zbl 1115.31001Heinonen, Juha; Kilpeläinen, Tero; Martio, Olli 220 2006 Moduli in modern mapping theory. Zbl 1175.30020Martio, Olli; Ryazanov, Vladimir; Srebro, Uri; Yakubov, Eduard 177 2009 Injectivity theorems in plane and space. Zbl 0406.30013Martio, O.; Sarvas, J. 160 1979 Definitions for quasiregular mappings. Zbl 0189.09204Martio, O.; Rickman, S.; Väisälä, J. 110 1969 Quasiextremal distance domains and extension of quasiconformal mappings. Zbl 0596.30031Gehring, F. W.; Martio, O. 66 1985 Lusin’s condition (N) and mappings of the class \(W^{1,n}\). Zbl 0812.30007Malý, Jan; Martio, Olli 65 1995 Traces of Sobolev functions on fractal type sets and characterization of extension domains. Zbl 0877.46025Hajłasz, Piotr; Martio, Olli 60 1997 The Sobolev capacity on metric spaces. Zbl 0859.46023Kinnunen, Juha; Martio, Olli 59 1996 Distortion and singularities of quasiregular mappings. Zbl 0197.05702Martio, O.; Rickman, S.; Väisälä, J. 58 1970 Topological and metric properties of quasiregular mappings. Zbl 0223.30018Martio, O.; Rickman, S.; Väisälä, J. 58 1971 Lipschitz classes and quasiconformal mappings. Zbl 0584.30018Gehring, F. W.; Martio, O. 54 1985 Nonlinear potential theory of metric spaces. Zbl 1030.46040Kinnunen, Juha; Martio, Olli 51 2002 Sobolev spaces with zero boundary values on metric spaces. Zbl 0962.46021Kipeläinen, Tero; Kinnunen, Juha; Martio, Olli 50 2000 On conformal dilatation in space. Zbl 1133.30319Bishop, Christopher J.; Gutlyanskiĭ, Vladimir Ya.; Martio, Olli; Vuorinen, Matti 49 2003 The Cantor function. Zbl 1098.26006Dovgoshey, O.; Martio, O.; Ryazanov, V.; Vuorinen, M. 48 2006 Two theorems of N. Wiener for solutions of quasilinear elliptic equations. Zbl 0607.35042Lindqvist, P.; Martio, O. 45 1985 Mappings with finite length distortion. Zbl 1084.30021Martio, O.; Ryazanov, V.; Srebro, U.; Yakubov, E. 45 2004 On harmonic quasiconformal mappings. Zbl 0162.37902Martio, O. 43 1968 Infinitesimal geometry of quasiconformal and bi-Lipschitz mappings in the plane. Zbl 1276.30002Bojarski, Bogdan; Gutlyanskii, Vladimir; Martio, Olli; Ryazanov, Vladimir 36 2013 Whitney cubes, p-capacity, and Minkowski content. Zbl 0632.30023Martio, O.; Vuorinen, M. 34 1987 On the degenerate Beltrami equation. Zbl 1066.30021Gutlyanskii, V.; Martio, O.; Sugawa, T.; Vuorinen, M. 33 2005 Hardy’s inequalities for Sobolev functions. Zbl 0909.42014Kinnunen, Juha; Martio, Olli 31 1997 Definitions for uniform domains. Zbl 0469.30017Martio, O. 31 1980 Conformally invariant variational integrals. Zbl 0518.30024Granlund, S.; Lindqvist, P.; Martio, O. 30 1983 Potential theory of quasiminimizers. Zbl 1035.31007Kinnunen, Juha; Martio, Olli 30 2003 Elliptic equations and maps of bounded length distortion. Zbl 0632.35021Martio, O.; Väisälä, J. 29 1988 On \(Q\)-homeomorphisms. Zbl 1071.30019Martio, O.; Ryazanov, V.; Srebro, U.; Yakubov, E. 25 2005 Lusin’s condition (N) and mappings with nonnegative Jacobians. Zbl 0807.46032Martio, O.; Ziemer, William P. 24 1992 John domains, bilipschitz balls and Poincaré inequality. Zbl 0652.30012Martio, O. 24 1988 Note on the PWB-method in the nonlinear case. Zbl 0633.31004Granlund, S.; Lindqvist, P.; Martio, O. 21 1986 Quasilines and conformal mappings. Zbl 0677.30012Fernández, José L.; Heinonen, Juha; Martio, Olli 21 1989 Choquet property for the Sobolev capacity in metric spaces. Zbl 0992.46023Kinnunen, Juha; Martio, Olli 21 2000 Periodic quasimeromorphic mappings in \(R^n\). Zbl 0317.30025Martio, Olli; Srebro, Uri 19 1975 Quasihyperbolic geodesics in John domains. Zbl 0702.30007Gehring, F. W.; Hag, K.; Martio, O. 18 1989 Stability in obstacle problems. Zbl 0839.35050Li, Gongbao; Martio, O. 16 1994 Sobolev space properties of superharmonic functions on metric spaces. Zbl 1042.31005Kinnunen, Juha; Martio, Olli 15 2003 A capacity inequality for quasiregular mappings. Zbl 0202.07402Martio, O. 14 1970 Quasiminimizers in one dimension: integrability of the derivate, inverse function and obstacle problems. Zbl 1150.49016Martio, O.; Sbordone, Carlo 14 2007 BMO and injectivity of space quasiregular mappings. Zbl 0935.30016Martio, Olli; Ryazanov, Vladimir; Vuorinen, Matti 14 1999 Harmonic morphisms in nonlinear potential theory. Zbl 0776.31007Heinonen, J.; Kilpeläinen, T.; Martio, O. 13 1992 F-harmonic measure in space. Zbl 0468.30015Granlund, S.; Lindqvist, P.; Martio, O. 13 1982 Local and global integrability of gradients in obstacle problems. Zbl 0803.35059Li, Gongbao; Martio, Olli 12 1994 Boundary behavior of quasiregular mappings. Zbl 0266.30029Martio, O.; Rickman, S. 12 1972 Removability theorems for solutions of degenerate elliptic partial differential equations. Zbl 0845.35015Koskela, Pekka; Martio, Olli 11 1993 On convergence theorems for space quasiregular mappings. Zbl 0907.30024Gutlyanskij, V. Ya.; Martio, O.; Ryazanov, V. I.; Vuorinen, M. 11 1998 \(Q\)-homeomorphisms. Zbl 1069.30039Martio, O.; Ryazanov, V.; Srebro, U.; Yakubov, E. 11 2004 Reflection principle for solutions of elliptic partial differential equations and quasiregular mappings. Zbl 0473.30016Martio, O. 11 1981 Infinitesimal geometry of quasilinear mappings. Zbl 0938.30014Gutlyanskij, V. Ya.; Martio, O.; Ryazanov, V. I.; Vuorinen, M. 11 2000 Products of metric spaces, covering numbers, packing numbers, and characterizations of ultrametric spaces. Zbl 1212.54088Dovgoshey, Oleksiy; Martio, Olli 10 2009 Blow up of balls and coverings in metric spaces. Zbl 1155.54017Dovgoshey, Oleksiy; Martio, Olli 10 2008 Counterexamples for unique continuation. Zbl 0653.30013Martio, Olli 10 1988 Rotation estimates and spirals. Zbl 0981.30014Gutlyanskii, Vladimir; Martio, Olli 10 2001 On existence and uniqueness of degenerate Beltrami equation. Zbl 1066.30022Martio, Olli; Miklyukov, Vladimir 10 2004 Large solutions of quasilinear elliptic equations in the degenrate case. Zbl 0960.35029Martio, Olli; Porru, Giovanni 10 1999 Tangent spaces to general metric spaces. Zbl 1265.54117Dovgoshey, Oleksiy; Martio, Olli 10 2011 Stability and higher integrability of derivatives of solutions in double obstacle problems. Zbl 1064.35056Li, Gongbao; Martio, O. 9 2002 On local injectivity and asymptotic linearity of quasiregular mappings. Zbl 0893.30012Gutlyanskiĭ, V. Ya.; Martio, O.; Ryazanov, V. I.; Vuorinen, M. 9 1998 Automorphic quasimeromorphic mappings in \(R^n\). Zbl 0329.30012Martio, Olli; Srebro, Uri 9 1975 Conformality of a quasiconformal mapping at a point. Zbl 1070.30007Gutlyanskiĭ, Vladimir; Martio, Olli 9 2003 Stability of solutions of varying degenerate elliptic equations. Zbl 0928.35071Li, Gongbao; Martio, Olli 9 1998 Equicontinuity theorem with an application to variational integrals. Zbl 0357.30017Martio, O. 8 1975 Density conditions in the n-capacity. Zbl 0365.30014Martio, O.; Sarvas, J. 8 1977 Functions transferring metrics to metrics. Zbl 1276.54020Dovgoshey, O.; Martio, O. 8 2013 Quasidisks and the Hardy-Littlewood property. Zbl 0574.30026Gehring, F. W.; Martio, O. 7 1983 Harnack’s principle for quasiminimizers. Zbl 1254.49010Kinnunen, Juha; Marola, Niko; Martio, O. 7 2007 Fine topology and quasilinear elliptic equations. Zbl 0659.35038Heinonen, J.; Kilpeläinen, T.; Martio, O. 7 1989 Some remarks on an existence problem for degenerate elliptic systems. Zbl 1069.30034Martio, Olli; Miklyukov, Vladimir; Vuorinen, Matti 7 2005 Capacity and measure densities. Zbl 0408.31008Martio, O. 7 1979 Locally injective automorphic mappings in \(\mathbb{R}^n\). Zbl 0953.30010Martio, O.; Srebro, U. 7 1999 Quasihyperbolic geodesics in convex domains. II. Zbl 1246.30041Martio, Olli; Väisälä, Jussi 7 2011 Functions of bounded variation and curves in metric measure spaces. Zbl 1360.26010Martio, Olli 6 2016 Phragmén-Lindelöf’s and Lindelöf’s theorems. Zbl 0594.30022Granlund, S.; Lindqvist, P.; Martio, O. 6 1985 Global \(L^ p\)-integrability of the derivative of a quasiconformal mapping. Zbl 0601.30024Martio, O.; Väisälä, J. 6 1988 Reflection principle for quasiminimizers. Zbl 1183.31003Martio, Olli 6 2009 Pasting lemmas and characterizations of boundary regularity for quasiminimizers. Zbl 1192.31001Björn, Anders; Martio, Olli 6 2009 On the integrability of the derivative of a quasiregular mapping. Zbl 0296.30019Martio, O. 6 1974 On the theory of \(Q(x)\)-homeomorphisms. Zbl 1074.30020Martio, O.; Ryazanov, V.; Srebro, U.; Yakubov, E. 6 2001 Fuglede’s theorem in variable exponent Sobolev space. Zbl 1070.46023Harjulehto, Petteri; Hästö, Peter; Martio, Olli 6 2004 On the local behaviour of quasi-regular space mappings. Zbl 0932.30017Vuorinen, M.; Martio, O.; Ryazanov, V. I. 6 1998 Quasiregular mappings and \(\mathcal W\mathcal T\)-classes of differential forms on Riemannian manifolds. Zbl 1063.30023Franke, D.; Martio, O.; Miklyukov, V. M.; Vuorinen, M.; Wisk, R. 5 2002 Boundary Hölder continuity and quasiconformal mappings. Zbl 0755.30026Martio, Olli; Näkki, Raimo 5 1991 Regularity and polar sets for supersolutions of certain degenerate elliptic equations. Zbl 0678.35025Lindqvist, P.; Martio, O. 5 1988 Modulus in Banach function spaces. Zbl 1396.30010Honzlová Exnerová, Vendula; Malý, Jan; Martio, Olli 5 2017 ACL homeomorphisms and linear dilatation. Zbl 0990.30014Kallunki, S.; Martio, O. 5 2002 On the existence of automorphic quasimeromorphic mappings in \(R^n\). Zbl 0383.30010Martio, O.; Srebro, U. 5 1977 Quasiminimizing properties of solutions to Riccati type equations. Zbl 1321.35025Martio, Olli 5 2013 Quasilinear Riccati type equations and quasiminimizers. Zbl 1218.35099Martio, O. 4 2011 On \(k\)-periodic quasiregular mappings in \(R^n\). Zbl 0325.30025Martio, O. 4 1975 Removability theorems for quasiregular mappings. Zbl 0717.30015Koskela, P.; Martio, O. 4 1990 Capacity and potential estimates for quasiminimizers. Zbl 1275.31003Martio, Olli 4 2011 The space of functions of bounded variation on curves in metric measure spaces. Zbl 1338.26006Martio, O. 4 2016 Functions of bounded variation and the \(AM\)-modulus in \(\mathbb{R}^n\). Zbl 1403.30023Honzlová Exnerová, Vendula; Malý, Jan; Martio, Olli 4 2018 Estimates for F-harmonic measures and \(\emptyset ksendal's\) theorem for quasiconformal mappings. Zbl 0643.35022Heinonen, J.; Martio, O. 3 1987 Measure properties of the branch set and its image of quasiregular mappings. Zbl 0265.30027Martio, O.; Rickman, S. 3 1973 On some properties of quasiplanes. Zbl 1030.30019Martio, O.; Miklyukov, V.; Ponnusamy, S.; Vuorinen, M. 3 2002 Metrization of weighted graphs. Zbl 1272.05031Dovgoshey, Oleksiy; Martio, Olli; Vuorinen, Matti 3 2013 Fluid flow in a medium distorted by a quasiconformal map can produce fractal boundaries. Zbl 0877.76073Martio, Olli; Øksendal, Bernt 2 1996 On the asymptotic behavior of quasiconformal mappings in space. Zbl 0892.30021Gutlyanskij, V. Ya.; Martio, O.; Ryazanov, V. I.; Vuorinen, M. 2 1998 Critical points of \(A\)-solutions of quasilinear elliptic equations. Zbl 0964.35062Martio, O.; Miklyukov, V. M.; Vuorinen, M. 2 1999 Plans on measures and AM-modulus. Zbl 1484.46041Honzlová Exnerová, Vendula; Kalenda, Ondřej F. K.; Malý, Jan; Martio, Olli 1 2021 Functions of bounded variation and the \(AM\)-modulus in \(\mathbb{R}^n\). Zbl 1403.30023Honzlová Exnerová, Vendula; Malý, Jan; Martio, Olli 4 2018 Nonlinear potential theory of degenerate elliptic equations. With a new preface, corrigenda, and epilogue consisting of other new material. Reprint of the 2006 edition. Zbl 1418.31001Heinonen, Juha; Kilpeläinen, Tero; Martio, Olli 1 2018 Modulus in Banach function spaces. Zbl 1396.30010Honzlová Exnerová, Vendula; Malý, Jan; Martio, Olli 5 2017 Functions of bounded variation and curves in metric measure spaces. Zbl 1360.26010Martio, Olli 6 2016 The space of functions of bounded variation on curves in metric measure spaces. Zbl 1338.26006Martio, O. 4 2016 Infinitesimal geometry of quasiconformal and bi-Lipschitz mappings in the plane. Zbl 1276.30002Bojarski, Bogdan; Gutlyanskii, Vladimir; Martio, Olli; Ryazanov, Vladimir 36 2013 Functions transferring metrics to metrics. Zbl 1276.54020Dovgoshey, O.; Martio, O. 8 2013 Quasiminimizing properties of solutions to Riccati type equations. Zbl 1321.35025Martio, Olli 5 2013 Metrization of weighted graphs. Zbl 1272.05031Dovgoshey, Oleksiy; Martio, Olli; Vuorinen, Matti 3 2013 Tangent spaces to general metric spaces. Zbl 1265.54117Dovgoshey, Oleksiy; Martio, Olli 10 2011 Quasihyperbolic geodesics in convex domains. II. Zbl 1246.30041Martio, Olli; Väisälä, Jussi 7 2011 Quasilinear Riccati type equations and quasiminimizers. Zbl 1218.35099Martio, O. 4 2011 Capacity and potential estimates for quasiminimizers. Zbl 1275.31003Martio, Olli 4 2011 On a theorem of Lindelöf. Zbl 1252.30017Gutlyanskiĭ, Vladimir; Martio, Olli; Ryazanov, Vladimir 2 2011 Wiman and Arima theorems for quasiregular mappings. Zbl 1226.30025Martio, O.; Miklyukov, V. M.; Vuorinen, M. 2 2010 Ahlfors theorems for differential forms. Zbl 1211.30039Martio, O.; Miklyukov, V. M.; Vuorinen, M. 1 2010 Moduli in modern mapping theory. Zbl 1175.30020Martio, Olli; Ryazanov, Vladimir; Srebro, Uri; Yakubov, Eduard 177 2009 Products of metric spaces, covering numbers, packing numbers, and characterizations of ultrametric spaces. Zbl 1212.54088Dovgoshey, Oleksiy; Martio, Olli 10 2009 Reflection principle for quasiminimizers. Zbl 1183.31003Martio, Olli 6 2009 Pasting lemmas and characterizations of boundary regularity for quasiminimizers. Zbl 1192.31001Björn, Anders; Martio, Olli 6 2009 Blow up of balls and coverings in metric spaces. Zbl 1155.54017Dovgoshey, Oleksiy; Martio, Olli 10 2008 Nonlinear potential theory in metric spaces. Zbl 1169.31300Martio, Olli 1 2008 Quasiminimizers in one dimension: integrability of the derivate, inverse function and obstacle problems. Zbl 1150.49016Martio, O.; Sbordone, Carlo 14 2007 Harnack’s principle for quasiminimizers. Zbl 1254.49010Kinnunen, Juha; Marola, Niko; Martio, O. 7 2007 On quasiplanes in Euclidean spaces. Zbl 1111.30013Martio, O.; Miklyukov, V. M.; Vuorinen, M. 1 2007 Nonlinear potential theory of degenerate elliptic equations. Unabridged republication of the 1993 original. Zbl 1115.31001Heinonen, Juha; Kilpeläinen, Tero; Martio, Olli 220 2006 The Cantor function. Zbl 1098.26006Dovgoshey, O.; Martio, O.; Ryazanov, V.; Vuorinen, M. 48 2006 On the degenerate Beltrami equation. Zbl 1066.30021Gutlyanskii, V.; Martio, O.; Sugawa, T.; Vuorinen, M. 33 2005 On \(Q\)-homeomorphisms. Zbl 1071.30019Martio, O.; Ryazanov, V.; Srebro, U.; Yakubov, E. 25 2005 Some remarks on an existence problem for degenerate elliptic systems. Zbl 1069.30034Martio, Olli; Miklyukov, Vladimir; Vuorinen, Matti 7 2005 Functions monotone close to boundary. Zbl 1099.31004Martio, Olli; Miklyukov, Vladimir; Vuorinen, Matti 1 2005 Mappings with finite length distortion. Zbl 1084.30021Martio, O.; Ryazanov, V.; Srebro, U.; Yakubov, E. 45 2004 \(Q\)-homeomorphisms. Zbl 1069.30039Martio, O.; Ryazanov, V.; Srebro, U.; Yakubov, E. 11 2004 On existence and uniqueness of degenerate Beltrami equation. Zbl 1066.30022Martio, Olli; Miklyukov, Vladimir 10 2004 Fuglede’s theorem in variable exponent Sobolev space. Zbl 1070.46023Harjulehto, Petteri; Hästö, Peter; Martio, Olli 6 2004 Boundary accessibility of a domain quasiconformally equivalent to a ball. Zbl 1040.30010Martio, Olli; Näkki, Raimo 2 2004 On conformal dilatation in space. Zbl 1133.30319Bishop, Christopher J.; Gutlyanskiĭ, Vladimir Ya.; Martio, Olli; Vuorinen, Matti 49 2003 Potential theory of quasiminimizers. Zbl 1035.31007Kinnunen, Juha; Martio, Olli 30 2003 Sobolev space properties of superharmonic functions on metric spaces. Zbl 1042.31005Kinnunen, Juha; Martio, Olli 15 2003 Conformality of a quasiconformal mapping at a point. Zbl 1070.30007Gutlyanskiĭ, Vladimir; Martio, Olli 9 2003 On the conformality of a quasiconformal mapping at a point. Zbl 1123.30011Gutlyanskii, V. Ya.; Martio, O. 1 2003 Generalized Wiman and Arima theorems for \(n\)-subharmonic functions on cones. Zbl 1048.31007Martio, Olli; Miklyukov, Vladimir; Vuorinen, Matti 1 2003 Nonlinear potential theory of metric spaces. Zbl 1030.46040Kinnunen, Juha; Martio, Olli 51 2002 Stability and higher integrability of derivatives of solutions in double obstacle problems. Zbl 1064.35056Li, Gongbao; Martio, O. 9 2002 Quasiregular mappings and \(\mathcal W\mathcal T\)-classes of differential forms on Riemannian manifolds. Zbl 1063.30023Franke, D.; Martio, O.; Miklyukov, V. M.; Vuorinen, M.; Wisk, R. 5 2002 ACL homeomorphisms and linear dilatation. Zbl 0990.30014Kallunki, S.; Martio, O. 5 2002 On some properties of quasiplanes. Zbl 1030.30019Martio, O.; Miklyukov, V.; Ponnusamy, S.; Vuorinen, M. 3 2002 On regularity of quasiconformal curves. Zbl 1216.30025Gutlyanskiĭ, Vladimir; Martio, Olli 2 2002 On Hölder continuity of quasiconformal maps with VMO dilatation. Zbl 1021.30018Gutlyanskij, V.; Martio, O.; Vuorinen, M. 1 2002 Rotation estimates and spirals. Zbl 0981.30014Gutlyanskii, Vladimir; Martio, Olli 10 2001 On the theory of \(Q(x)\)-homeomorphisms. Zbl 1074.30020Martio, O.; Ryazanov, V.; Srebro, U.; Yakubov, E. 6 2001 Harnack’s inequality for \(p\)-harmonic functions on Riemannian manifolds for different exhaustions. Zbl 1043.31006Martio, O.; Miklyukov, V. M.; Vuorinen, M. 1 2001 Sobolev spaces with zero boundary values on metric spaces. Zbl 0962.46021Kipeläinen, Tero; Kinnunen, Juha; Martio, Olli 50 2000 Choquet property for the Sobolev capacity in metric spaces. Zbl 0992.46023Kinnunen, Juha; Martio, Olli 21 2000 Infinitesimal geometry of quasilinear mappings. Zbl 0938.30014Gutlyanskij, V. Ya.; Martio, O.; Ryazanov, V. I.; Vuorinen, M. 11 2000 Maximal operator and superharmonicity. Zbl 0969.42008Kinnunen, Juha; Martio, Olli 2 2000 Modern tools in the theory of quasiconformal maps. Zbl 0997.30014Martio, Olli 2 2000 Stability of harmonic measures. Zbl 1024.31008Li, Gongbao; Martio, O. 1 2000 On the weak Lipschitz condition for quasiconformal mappings. Zbl 1044.30010Vuorinen, M.; Gutlyanskij, V. Ya.; Martio, O. 1 2000 BMO and injectivity of space quasiregular mappings. Zbl 0935.30016Martio, Olli; Ryazanov, Vladimir; Vuorinen, Matti 14 1999 Large solutions of quasilinear elliptic equations in the degenrate case. Zbl 0960.35029Martio, Olli; Porru, Giovanni 10 1999 Locally injective automorphic mappings in \(\mathbb{R}^n\). Zbl 0953.30010Martio, O.; Srebro, U. 7 1999 Critical points of \(A\)-solutions of quasilinear elliptic equations. Zbl 0964.35062Martio, O.; Miklyukov, V. M.; Vuorinen, M. 2 1999 Normal families, multiplicity and the branch set of quasiregular maps. Zbl 0923.30015Martio, O.; Srebro, U.; Väisälä, J. 2 1999 On convergence theorems for space quasiregular mappings. Zbl 0907.30024Gutlyanskij, V. Ya.; Martio, O.; Ryazanov, V. I.; Vuorinen, M. 11 1998 On local injectivity and asymptotic linearity of quasiregular mappings. Zbl 0893.30012Gutlyanskiĭ, V. Ya.; Martio, O.; Ryazanov, V. I.; Vuorinen, M. 9 1998 Stability of solutions of varying degenerate elliptic equations. Zbl 0928.35071Li, Gongbao; Martio, Olli 9 1998 On the local behaviour of quasi-regular space mappings. Zbl 0932.30017Vuorinen, M.; Martio, O.; Ryazanov, V. I. 6 1998 On the asymptotic behavior of quasiconformal mappings in space. Zbl 0892.30021Gutlyanskij, V. Ya.; Martio, O.; Ryazanov, V. I.; Vuorinen, M. 2 1998 Morrey’s lemma on Riemannian manifolds. Zbl 0928.46017Martio, O.; Miklyukov, V. M.; Vuorinen, M. 2 1998 The local behavior of quasiconformal maps in space. Zbl 0959.30011Vuorinen, M.; Gutlyanskij, V. Ya.; Martio, O.; Ryazanov, V. I. 1 1998 Second order obstacle problems for vectorial functions and integrands with subquadratic growth. Zbl 0910.49002Fuchs, M.; Li, Gongbao; Martio, O. 1 1998 Traces of Sobolev functions on fractal type sets and characterization of extension domains. Zbl 0877.46025Hajłasz, Piotr; Martio, Olli 60 1997 Hardy’s inequalities for Sobolev functions. Zbl 0909.42014Kinnunen, Juha; Martio, Olli 31 1997 The Sobolev capacity on metric spaces. Zbl 0859.46023Kinnunen, Juha; Martio, Olli 59 1996 Fluid flow in a medium distorted by a quasiconformal map can produce fractal boundaries. Zbl 0877.76073Martio, Olli; Øksendal, Bernt 2 1996 Differential forms and quasiregular mappings on Riemannian manifolds. Zbl 0899.58065Martio, Olli; Miklyukov, Vladimir; Vuorinen, Matti 1 1996 The Phragmen-Lindelöf principle for quasiregular mappings of manifolds and the isoperimetry. Zbl 0886.30020Vuorinen, M.; Martio, O.; Miklyukov, V. M. 1 1996 Lusin’s condition (N) and mappings of the class \(W^{1,n}\). Zbl 0812.30007Malý, Jan; Martio, Olli 65 1995 On the fusion problem for degenerate elliptic equations. Zbl 0824.35040Kilpeläinen, T.; Koskela, P.; Martio, O. 1 1995 Stability in obstacle problems. Zbl 0839.35050Li, Gongbao; Martio, O. 16 1994 Local and global integrability of gradients in obstacle problems. Zbl 0803.35059Li, Gongbao; Martio, Olli 12 1994 Nonlinear potential theory of degenerate elliptic equations. Zbl 0780.31001Heinonen, Juha; Kilpeläinen, Tero; Martio, Olli 598 1993 Removability theorems for solutions of degenerate elliptic partial differential equations. Zbl 0845.35015Koskela, Pekka; Martio, Olli 11 1993 Bounded turning and passability. Zbl 0786.30017Martio, O.; Väisälä, J. 2 1993 Lusin’s condition (N) and mappings with nonnegative Jacobians. Zbl 0807.46032Martio, O.; Ziemer, William P. 24 1992 Harmonic morphisms in nonlinear potential theory. Zbl 0776.31007Heinonen, J.; Kilpeläinen, T.; Martio, O. 13 1992 Partial differential equations and quasiregular mappings. Zbl 0794.35052Martio, Olli 1 1992 Boundary Hölder continuity and quasiconformal mappings. Zbl 0755.30026Martio, Olli; Näkki, Raimo 5 1991 Removability theorems for quasiregular mappings. Zbl 0717.30015Koskela, P.; Martio, O. 4 1990 Quasilines and conformal mappings. Zbl 0677.30012Fernández, José L.; Heinonen, Juha; Martio, Olli 21 1989 Quasihyperbolic geodesics in John domains. Zbl 0702.30007Gehring, F. W.; Hag, K.; Martio, O. 18 1989 Fine topology and quasilinear elliptic equations. Zbl 0659.35038Heinonen, J.; Kilpeläinen, T.; Martio, O. 7 1989 Potential theoretic aspects of nonlinear elliptic partial differential equations. Zbl 0684.35008Martio, Olli 2 1989 Sets of zero elliptic harmonic measures. Zbl 0741.31004Martio, O. 1 1989 Elliptic equations and maps of bounded length distortion. Zbl 0632.35021Martio, O.; Väisälä, J. 29 1988 John domains, bilipschitz balls and Poincaré inequality. Zbl 0652.30012Martio, O. 24 1988 Counterexamples for unique continuation. Zbl 0653.30013Martio, Olli 10 1988 Global \(L^ p\)-integrability of the derivative of a quasiconformal mapping. Zbl 0601.30024Martio, O.; Väisälä, J. 6 1988 ...and 34 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,392 Authors 80 Sevost’yanov, Yevgen Oleksandrovych 49 Koskela, Pekka 49 Ryazanov, Vladimir Il’ich 48 Salimov, Ruslan Radikovich 47 Martio, Olli 43 Björn, Anders 43 Björn, Jana 39 Vuorinen, Matti Keijo Kustaa 37 Shanmugalingam, Nageswari 23 Gutlyanskiĭ, Vladimir Ya. 23 Heinonen, Juha 21 Ponnusamy, Saminathan 20 Kalaj, David 19 Kilpeläinen, Tero 19 Vodop’yanov, Sergeĭ Konstantinovich 18 Golberg, Anatoly 18 Nguyen Cong Phuc 18 Xiao, Jie 17 Dovgoshey, Oleksiy Alfredovich 17 Gol’dshtein, Vladimir Mikhailovich 16 Ding, Shusen 16 Lewis, John L. 16 Parviainen, Mikko 16 Ukhlov, Alexander Dadar-Oolovich 16 Wang, Xiantao 15 Afanas’eva, Elena Sergeevna 15 Holopainen, Ilkka 15 Iwaniec, Tadeusz 15 Lindqvist, Peter 15 Malý, Jan 15 Mingione, Giuseppe 15 Onninen, Jani 15 Srebro, Uri 14 Byun, Sun-Sig 14 Kinnunen, Juha 14 Li, Yaxiang 14 Marola, Niko 13 Kuusi, Tuomo 13 Miklyukov, Vladimir Mikhaiĭlovich 13 Shimomura, Tetsu 13 Verbitsky, Igor E. 12 Guo, Changyu 12 Harjulehto, Petteri 12 Hästö, Peter A. 12 Korte, Riikka 12 Lahti, Panu 12 Lehrbäck, Juha 12 Pankka, Pekka 12 Skvortsov, Sergei Aleksandrovich 12 Väisälä, Jussi 12 Vogel, Andrew L. 12 Wang, Lihe 12 Yakubov, Eduard H. 11 Adamowicz, Tomasz 11 Akman, Murat 11 Fletcher, Alastair N. 11 Hajłasz, Piotr 11 Hencl, Stanislav 11 Mizuta, Yoshihiro 11 Rasila, Antti 11 Zhou, Qingshan 10 Bao, Gejun 10 Bucur, Dorin 10 Herron, David A. 10 Hurri-Syrjānen, Ritva 10 Lukkari, Teemu 10 Vähäkangas, Antti V. 9 Cavalheiro, Albo Carlos 9 Dal Maso, Gianni 9 Gao, Hongya 9 Jiang, Renjin 9 Kovtonyuk, D. A. 9 Manfredi, Juan J. 9 Rajala, Kai 9 Rickman, Seppo Uolevi 9 Rodríguez García, José Manuel 8 Astala, Kari 8 Fernández-Sánchez, Juan 8 Hirata, Kentaro 8 Hofmann, Steve 8 Huang, Manzi 8 Nolder, Craig A. 8 Otárola, Enrique 8 Petrov, Evgenii Aleksandrovich 8 Tuominen, Heli 8 Xing, Yuming 8 Zhong, Xiao 7 Chen, Shaolin 7 Habermann, Jens 7 Latvala, Visa 7 Li, Gongbao 7 Nakai, Mitsuru 7 Nyström, Kaj 7 Passarelli di Napoli, Antonia 7 Sahoo, Swadesh Kumar 7 Sbordone, Carlo 7 Yang, Shanshuang 6 Adimurthi, Karthik 6 Alkhutov, Yuriy Alexandrovich 6 Azzam, Jonas ...and 1,292 more Authors all top 5 Cited in 271 Serials 101 Journal of Mathematical Analysis and Applications 81 Nonlinear Analysis. Theory, Methods & Applications. 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Serie V 9 Boundary Value Problems 9 Analysis and Geometry in Metric Spaces 8 Inventiones Mathematicae 8 SIAM Journal on Mathematical Analysis 8 Communications on Pure and Applied Analysis 7 Computers & Mathematics with Applications 7 Annales de l’Institut Fourier 7 Journal of the Mathematical Society of Japan 7 Results in Mathematics 7 Tôhoku Mathematical Journal. Second Series 7 Acta Mathematica Sinica. English Series 7 Comptes Rendus. Mathématique. Académie des Sciences, Paris 7 Science China. Mathematics 6 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 6 Illinois Journal of Mathematics 6 Michigan Mathematical Journal 6 Proceedings of the Japan Academy. Series A 6 Advances in Applied Clifford Algebras 6 Abstract and Applied Analysis 6 Sibirskie Èlektronnye Matematicheskie Izvestiya 6 Journal of Fixed Point Theory and Applications 6 Advances in Nonlinear Analysis 5 Applicable Analysis 5 Rocky Mountain Journal of Mathematics 5 Czechoslovak Mathematical Journal 5 Journal für die Reine und Angewandte Mathematik 5 Bulletin des Sciences Mathématiques 5 Doklady Mathematics 5 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 5 Matematychni Studiï 5 Revista Matemática Complutense 5 \(p\)-Adic Numbers, Ultrametric Analysis, and Applications 4 Bulletin of the Australian Mathematical Society 4 Mathematical Methods in the Applied Sciences 4 Mathematical Proceedings of the Cambridge Philosophical Society 4 Applied Mathematics and Optimization 4 Collectanea Mathematica 4 Publications Mathématiques 4 Zeitschrift für Analysis und ihre Anwendungen 4 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 4 Stochastic Processes and their Applications 4 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 4 Expositiones Mathematicae 4 Applied Mathematics. Series B (English Edition) 4 Filomat 4 Positivity 4 Advanced Nonlinear Studies 4 Vladikavkazskiĭ Matematicheskiĭ Zhurnal 4 Mediterranean Journal of Mathematics 4 Fixed Point Theory and Applications 4 Journal of Function Spaces 3 Communications in Mathematical Physics 3 The Annals of Probability 3 Indiana University Mathematics Journal 3 Integral Equations and Operator Theory ...and 171 more Serials all top 5 Cited in 60 Fields 722 Partial differential equations (35-XX) 709 Functions of a complex variable (30-XX) 406 Potential theory (31-XX) 360 Functional analysis (46-XX) 175 Real functions (26-XX) 141 Calculus of variations and optimal control; optimization (49-XX) 92 Global analysis, analysis on manifolds (58-XX) 89 Measure and integration (28-XX) 87 Differential geometry (53-XX) 76 Harmonic analysis on Euclidean spaces (42-XX) 74 Operator theory (47-XX) 44 General topology (54-XX) 38 Dynamical systems and ergodic theory (37-XX) 35 Probability theory and stochastic processes (60-XX) 31 Mechanics of deformable solids (74-XX) 27 Several complex variables and analytic spaces (32-XX) 24 Fluid mechanics (76-XX) 22 Numerical analysis (65-XX) 18 Approximations and expansions (41-XX) 18 Manifolds and cell complexes (57-XX) 13 Convex and discrete geometry (52-XX) 12 Abstract harmonic analysis (43-XX) 11 Ordinary differential equations (34-XX) 10 Geometry (51-XX) 9 Topological groups, Lie groups (22-XX) 9 Optics, electromagnetic theory (78-XX) 9 Biology and other natural sciences (92-XX) 7 Difference and functional equations (39-XX) 7 Integral equations (45-XX) 6 Combinatorics (05-XX) 6 Quantum theory (81-XX) 5 Number theory (11-XX) 5 Statistics (62-XX) 5 Information and communication theory, circuits (94-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Computer science (68-XX) 4 Mechanics of particles and systems (70-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 Mathematical logic and foundations (03-XX) 3 Algebraic geometry (14-XX) 3 Sequences, series, summability (40-XX) 3 Algebraic topology (55-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Systems theory; control (93-XX) 2 General and overarching topics; collections (00-XX) 2 Group theory and generalizations (20-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Operations research, mathematical programming (90-XX) 1 History and biography (01-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 General algebraic systems (08-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Associative rings and algebras (16-XX) 1 Category theory; homological algebra (18-XX) 1 Special functions (33-XX) 1 Integral transforms, operational calculus (44-XX) 1 Relativity and gravitational theory (83-XX) 1 Geophysics (86-XX) 1 Mathematics education (97-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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