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JOURNALS // Trudy Matematicheskogo Instituta imeni V.A. Steklova // Archive
Trudy Mat. Inst. Steklova, 2020 Volume 308, Pages 7–27 (Mi tm4047)
This article is cited in 6 papers

Hölder Continuity and Harnack's Inequality for $p(x)$-Harmonic Functions

Yu. A. Alkhutova, M. D. Surnachevb

a Vladimir State University Named after Alexander and Nikolay Stoletovs, ul. Gor'kogo 87, Vladimir, 600000 Russia
b Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moscow, 125047 Russia

Abstract: A sufficient condition for a measurable exponent $p(x)$ is obtained that implies the Hölder continuity and Harnack's inequality for $p(x)$-harmonic functions.

UDC: 517.956.25

Received: April 1, 2019
Revised: August 13, 2019
Accepted: November 5, 2019

DOI: 10.4213/tm4047


 English version: Proceedings of the Steklov Institute of Mathematics, 2020, 308, 1–21

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© Steklov Math. Inst. of RAS, 2024