Yu. A. Alkhutov, A. G. Chechkina, “Many-dimensional Zaremba problem for an inhomogeneous <nobr>$p$</nobr>-Laplace equation”, Dokl. RAN. Math. Inf. Proc. Upr., 2022, Volume 505,Pages <nobr>37

This article is cited in 8 papers

MATHEMATICS

Many-dimensional Zaremba problem for an inhomogeneous $p$-Laplace equation

Yu. A. Alkhutov^a, A. G. Chechkina^bc

^a Vladimir State University, Vladimir, Russia
^b Lomonosov Moscow State University, Moscow, Russia
^c Institute of Mathematics with Computing Centre — Subdivision of the Ufa Federal Research Centre of the Russian Academy of Sciences, Ufa, Bashkortostan, Russia

Abstract: Higher integrability of the gradient of the solution to the Zaremba problem in a bounded Lipschitz many-dimensional domain for an inhomogeneous $p$-Laplace equation is proved.

Keywords: Zaremba problem, Meyers estimates, $p$-capacity, embedding theorems, higher integrability.

UDC: 517.954, 517.982

Presented: V. V. Kozlov
Received: 16.05.2022
Revised: 10.06.2022
Accepted: 15.06.2022

DOI: 10.31857/S2686954322040026