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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2020, Volume 60, Number 8, Pages 1329–1338
DOI: https://doi.org/10.31857/S0044466920080025 (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
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DOI: https://doi.org/10.31857/S0044466920080025
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.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00184
This work was supported by the Russian Foundation for Basic Research, project no. 19-01-00184.
Received: 19.11.2019
Revised: 15.12.2019
Accepted: 09.04.2020
English version:
Computational Mathematics and Mathematical Physics, 2020, Volume 60, Issue 8, Pages 1284–1293
DOI: https://doi.org/10.1134/S0965542520080023
Bibliographic databases:
Document Type: Article
UDC: 517.956.2
Language: Russian
Citation: Yu. A. Alkhutov, M. D. Surnachev, “Harnack inequality for the elliptic $p(x)$-Laplacian with a three-phase exponent $p(x)$”, Zh. Vychisl. Mat. Mat. Fiz., 60:8 (2020), 1329–1338; Comput. Math. Math. Phys., 60:8 (2020), 1284–1293
Citation in format AMSBIB
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