RUS
ENG
Full version
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. Alkhutov
a
,
M. D. Surnachev
bc
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
References
English version:
Computational Mathematics and Mathematical Physics, 2020,
60
:8,
1284–1293
Bibliographic databases:
©
Steklov Math. Inst. of RAS
, 2024