Dokl. RAN. Math. Inf. Proc. Upr., 2023 Volume 512, Pages 47–51
(Mi danma397)
MATHEMATICS On higher integrability of the gradient of solutions to the Zaremba problem for $p$ -Laplace equation Yu. A. Alkhutov a ,
C. D. Apice b ,
M. A. Kisatov c ,
A. G. Chechkina cd a Vladimir State University, Vladimir, Russian Federation b University of Salerno, Italia c Lomonosov Moscow State University, Moscow, Russian Federation d Institute of Mathematics with Computing Centre — Subdivision of the Ufa Federal Research Centre of the Russian Academy of Sciences, Ufa, Russian Federation Abstract:
A higher integrability of the gradient of a solution to the Zaremba problem in a bounded Lipschitz plane domain is proved for the inhomogeneous
$p$ -Laplace equation.
Keywords:
Zaremba problem, meyers estimates, $p$ -capacity, imbedding theorems, higher integrability.
UDC:
517.954 ,
517.982 Presented: V. V. Kozlov Received: 13.07.2022
Revised: 22.05.2023
Accepted: 30.05.2023
DOI:
10.31857/S268695432260046X
© , 2024
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