Yu. A. Alkhutov, M. D. Surnachev, “Behavior of solutions of the Dirichlet Problem for the $ p(x)$-Laplacian at a boundary point”, Algebra i Analiz, 31:2 (2019), 88–117; St. Petersburg Math. J., 31:2 (2019), 251

Algebra i Analiz

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Archive
	Impact factor

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

Algebra i Analiz:
Year:
Volume:
Issue:
Page:
	Find

Personal entry:
Login:
Password:
	Save password
	Enter
	Forgotten password?
	Register

Algebra i Analiz, 2019, Volume 31, Issue 2, Pages 88–117 (Mi aa1639)

This article is cited in 19 scientific papers (total in 19 papers)

Research Papers

Behavior of solutions of the Dirichlet Problem for the

p (x)

$p(x)$ -Laplacian at a boundary point

Yu. A. Alkhutov^a, M. D. Surnachev^b

^a Vladimir State University
^b Keldysh Institute of Applied Mathematics of Russian Academy of Sciences

Full-text PDF (321 kB) Citations (19)

References:

PDF

HTML

Abstract: The Dirichlet problem for the

p (x)

$p(x)$ -Laplacian with a continuous boundary function is treated. A sufficient condition is indicated for the regularity of a boundary point, and the modulus of continuity of solutions at this point is estimated.

Keywords: Wiener criterion, boundary regularity, Dirichlet problem, variable exponent,

p (x)

$p(x)$ -Laplacian.

Funding agency	Grant number
Ministry of Education and Science of the Russian Federation	1.3270.2017/4.6
Russian Foundation for Basic Research	19-01-00184_а
The work was supported by the Ministry of Education and Science of the Russian Federation (grant 1.3270.2017/4.6) and Russian Foundation for Basic Research (grant 19-01-00184-a)

Received: 31.10.2018

English version:
St. Petersburg Mathematical Journal, 2019, Volume 31, Issue 2, Pages 251–271
DOI: https://doi.org/10.1090/spmj/1595

Bibliographic databases:

Document Type: Article

MSC: Primary 35J57, 35J67, 35J92; Secondary 35J15

Language: Russian

Citation: Yu. A. Alkhutov, M. D. Surnachev, “Behavior of solutions of the Dirichlet Problem for the

p (x)

$p(x)$ -Laplacian at a boundary point”, Algebra i Analiz, 31:2 (2019), 88–117; St. Petersburg Math. J., 31:2 (2019), 251–271

Citation in format AMSBIB

\Bibitem{AlkSur19}

\by Yu.~A.~Alkhutov, M.~D.~Surnachev

\paper Behavior of solutions of the Dirichlet Problem for the $ p(x)$-Laplacian at a boundary point

\jour Algebra i Analiz

\yr 2019

\vol 31

\issue 2

\pages 88--117

\mathnet{http://mi.mathnet.ru/aa1639}

\elib{https://elibrary.ru/item.asp?id=46736881}

\transl

\jour St. Petersburg Math. J.

\yr 2019

\vol 31

\issue 2

\pages 251--271

\crossref{https://doi.org/10.1090/spmj/1595}

\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000515138700004}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85090379882}

Linking options:

https://www.mathnet.ru/eng/aa1639

https://www.mathnet.ru/eng/aa/v31/i2/p88

This publication is cited in the following 19 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)
Yu. A. Alkhutov, M. D. Surnachev, “Interior and Boundary Continuity of p(x)-Harmonic Functions”, J Math Sci, 283:5 (2024), 699
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
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”, J Math Sci, 273:3 (2023), 427
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
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)
Yu. A. Alkhutov, M. D. Surnachev, “A Variation on the p(x)-Laplace Equation”, J Math Sci, 268:3 (2022), 266
I. I. Skrypnik, M. V. Voitovych, “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
G. Mingione, V. Radulescu, “Recent developments in problems with nonstandard growth and nonuniform ellipticity”, J. Math. Anal. Appl., 501:1, SI (2021), 125197
M. A. Shan, I. I. Skrypnik, M. V. Voitovych, “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, “The Boundary Behavior of a Solution to the Dirichlet Problem for a Linear Degenerate Second Order Elliptic Equation”, J Math Sci, 259:2 (2021), 109
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
A. A. Kon'kov, “Geometric estimates of solutions of quasilinear elliptic inequalities”, Izv. Math., 84:6 (2020), 1056–1104
L. M. Kozhevnikova, “Renormalized solutions of elliptic equations with variable exponents and general measure data”, Sb. Math., 211:12 (2020), 1737–1776
Yu. A. Alkhutov, M. D. Surnachev, “The Boundary Behavior of a Solution to the Dirichlet Problem for the p-Laplacian with Weight Uniformly Degenerate on a Part of Domain with Respect to Small Parameter”, J Math Sci, 250:2 (2020), 183
Igor Skrypnik, Mykhailo Voitovych, “\mathfrak{B}_{1} classes of De Giorgi, Ladyzhenskaya, and Ural'tseva and their application to elliptic and parabolic equations with nonstandard growth”, UMB, 16:3 (2019), 403

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

Statistics & downloads:
Abstract page:	390
Full-text PDF :	60
References:	59
First page:	36

Registration to the website

Logotypes