Yu. A. Alkhutov, O. V. Krasheninnikova, “On the Continuity of Solutions to Elliptic Equations with Variable Order of Nonlinearity”, Differential equations and dynamical systems, Collected papers, Trudy Mat. Inst. Steklova, 261, MAIK Nauka/Interperiodica, Moscow, 2008, 7–15; Proc. Steklov Inst. Math., 261 (2008), 1

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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2008, Volume 261, Pages 7–15 (Mi tm735)

This article is cited in 24 scientific papers (total in 24 papers)

On the Continuity of Solutions to Elliptic Equations with Variable Order of Nonlinearity

Yu. A. Alkhutov, O. V. Krasheninnikova

Vladimir State Pedagogical University

Full-text PDF (183 kB) Citations (24)

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Abstract: We study the $p$-Laplacian with variable exponent $p(x)$ bounded away from unity and infinity. We obtain a sufficient condition on $p(x)$ under which all solutions of the $p$-Laplace equation are continuous at a fixed point of a domain, and find an estimate for the modulus of continuity of solutions.

Received in March 2007

English version:
Proceedings of the Steklov Institute of Mathematics, 2008, Volume 261, Pages 1–10
DOI: https://doi.org/10.1134/S0081543808020016

Bibliographic databases:

UDC: 517.956.25

Language: Russian

Citation: Yu. A. Alkhutov, O. V. Krasheninnikova, “On the Continuity of Solutions to Elliptic Equations with Variable Order of Nonlinearity”, Differential equations and dynamical systems, Collected papers, Trudy Mat. Inst. Steklova, 261, MAIK Nauka/Interperiodica, Moscow, 2008, 7–15; Proc. Steklov Inst. Math., 261 (2008), 1–10

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tm735

https://www.mathnet.ru/eng/tm/v261/p7

This publication is cited in the following 24 articles:

Igor Skrypnik, Yevgeniia Yevgenieva, “Harnack inequality for solutions of the p(x)-Laplace equation under the precise non-logarithmic Zhikov's conditions”, Calc. Var., 63:1 (2024)
Tran Thi Hanh, Cong Nhan Le, “A New De Giorgi class type related to the Caffarelli-Kohn-Nirenberg weights and Hölder continuity”, Journal of Mathematical Analysis and Applications, 2024, 128696
Mokhtar Naceri, “Variable exponents anisotropic nonlinear elliptic systems with Lp′→(⋅)-data”, Applicable Analysis, 2024, 1
Andrii S. Bychkov, Oleksandr V. Hadzhy, Yevhen S. Zozulia, “On the generalized weak Harnack inequality for non-negative super-solutions of quasilinear elliptic equations with absorption term”, J Math Sci, 282:1 (2024), 13
Yu. A. Alkhutov, M. D. Surnachev, “Interior and Boundary Continuity of p(x)-Harmonic Functions”, J Math Sci, 283:5 (2024), 699
Simone Ciani, Eurica Henriques, Igor I. Skrypnik, “The weak Harnack inequality for unbounded minimizers of elliptic functionals with generalized Orlicz growth”, Advances in Calculus of Variations, 2024
Andrii S. Bychkov, Oleksandr V. Hadzhy, Yevhen S. Zozulia, “On the generalized weak Harnack inequality for non-negative super-solutions of quasilinear elliptic equations with absorption term”, UMB, 21:1 (2024), 16
Mariia Savchenko, Igor Skrypnik, Yevgeniia Yevgenieva, “Harnack's inequality for degenerate double phase parabolic equations under the non-logarithmic Zhikov's condition”, J Math Sci, 273:3 (2023), 427
Ihor Skrypnik, Maria Savchenko, Yevgeniia Yevgenieva, “Weak Harnack inequality for unbounded solutions to the p(x)-Laplace equation under the precise non-logarithmic conditions”, Proc. IAMM NASU, 37 (2023), 48
Mariia Savchenko, Igor Skrypnik, Yevgeniia Yevgenieva, “Harnack's inequality for degenerate double phase parabolic equations under the non-logarithmic Zhikov's condition”, UMB, 20:1 (2023), 124
Skrypnik I.I., Voitovych M.V., “On the Continuity of Solutions of Quasilinear Parabolic Equations With Generalized Orlicz Growth Under Non-Logarithmic Conditions”, Ann. Mat. Pura Appl., 201:3 (2022), 1381–1416
Yu. A. Alkhutov, M. D. Surnachev, “A Variation on the p(x)-Laplace Equation”, J Math Sci, 268:3 (2022), 266
Igor I. Skrypnik, “Harnack's inequality for singular parabolic equations with generalized Orlicz growth under the non-logarithmic Zhikov's condition”, J. Evol. Equ., 22:2 (2022)
Skrypnik I.I., Voitovych M.V., “B-1 Classes of de Giorgi-Ladyzhenskaya-Ural'Tseva and Their Applications to Elliptic and Parabolic Equations With Generalized Orlicz Growth Conditions”, Nonlinear Anal.-Theory Methods Appl., 202 (2021), 112135
Yu. A. Alkhutov, M. D. Surnachev, “Vnutrennyaya i granichnaya nepreryvnost $p(x)$-garmonicheskikh funktsii”, Kraevye zadachi matematicheskoi fiziki i smezhnye voprosy teorii funktsii. 49, K yubileyu Grigoriya Aleksandrovicha SEREGINA, Zap. nauchn. sem. POMI, 508, POMI, SPb., 2021, 7–38
Shan M.A., Skrypnik I.I., Voitovych M.V., “Harnack'S Inequality For Quasilinear Elliptic Equations With Generalized Orlicz Growth”, Electron. J. Differ. Equ., 2021
Maria A. Shan, Igor I. Skrypnik, Mykhailo V. Voitovych, “Harnack's inequality for quasilinear elliptic equations with generalized Orlicz growth”, ejde, 2021:01-104 (2021), 27
Yu. A. Alkhutov, M. D. Surnachev, “Hölder Continuity and Harnack's Inequality for $p(x)$-Harmonic Functions”, Proc. Steklov Inst. Math., 308 (2020), 1–21
Yu. A. Alkhutov, M. D. Surnachev, “Harnack inequality for the elliptic $p(x)$-Laplacian with a three-phase exponent $p(x)$”, Comput. Math. Math. Phys., 60:8 (2020), 1284–1293
Igor I. Skrypnik, Mykhailo V. Voitovych, “$ {\mathfrak{B}}_1 $ classes of De Giorgi, Ladyzhenskaya, and Ural'tseva and their application to elliptic and parabolic equations with nonstandard growth”, J Math Sci, 246:1 (2020), 75

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Труды Математического института имени В. А. Стеклова

Proceedings of the Steklov Institute of Mathematics

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