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JOURNALS // Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki // Archive

Zh. Vychisl. Mat. Mat. Fiz., 2020 Volume 60, Number 8, Pages 1329–1338 (Mi zvmmf11114)

Harnack inequality for the elliptic $p(x)$-Laplacian with a three-phase exponent $p(x)$

Yu. A. Alkhutova, M. D. Surnachevbc

a Vladimir State University, Vladimir, 600000 Russia
b Federal Research Center Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, 125047 Russia
c National University of Science and Technology MISiS, Moscow, 119049 Russia

Abstract: For an elliptic $p(x)$-Laplacian with a piecewise constant three-phase exponent $p$ in the plane with three phases joining at a point, a Harnack inequality is proved and the Hölder continuity of the solution is established.

Key words: $p(x)$-Laplacian, Harnack inequality, Hölder continuity, Moser method, three-phase exponent.

UDC: 517.956.2

Received: 19.11.2019
Revised: 15.12.2019
Accepted: 09.04.2020

DOI: 10.31857/S0044466920080025


 English version:
Computational Mathematics and Mathematical Physics, 2020, 60:8, 1284–1293

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© Steklov Math. Inst. of RAS, 2024