This article is cited in 1 paper

MATHEMATICS

On the Zaremba problem for inhomogeneous $p$-Laplace equation with drift

Yu. A. Alkhutov^a, M. D. Surnachev^b, A. G. Chechkina<sup>cd

a</sup> Vladimir State University
^b Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow
^c Lomonosov Moscow State University
^d Institute of Mathematics with Computing Centre — Subdivision of the Ufa Federal Research Centre of the Russian Academy of Sciences, Ufa

Abstract: A higher integrability of the gradient of a solution to the Zaremba problem in a bounded Lipschitz domain is proved for the inhomogeneous $p$-Laplace equation with drift.

Keywords: Zaremba problem, Meyers estimates, $p$-capacity, imbedding theorems, higher integrability, critical indicator.

UDC: 517.954+517.982

Presented: V. V. Kozlov
Received: 25.12.2024
Revised: 31.01.2025
Accepted: 31.01.2025

DOI: 10.31857/S2686954325010016

 English version: Doklady Mathematics, 2025, 111:1, 1–5

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