This article is cited in 2 papers

Bojarski–Meyers estimate for a solution to the Zaremba problem for Poisson's equations with drift

Yu. A. Alkhutov^a, G. A. Chechkin<sup>bcd

a</sup> Vladimir State University, Vladimir, Russia
^b Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
^c Institute of Mathematics with Computing Centre, Ufa Federal Research Centre of the Russian Academy of Sciences, Ufa, Russia
^d Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

Abstract: An estimate for the increased integrability is obtained for the gradient of the solution to the Zaremba problem for Poisson's equation with lower-order terms in a bounded domain with Lipschitz boundary and frequent alternation of Dirichlet and Neumann conditions.
Bibliography: 22 titles.

Keywords: Bojarski–Meyers estimates, embedding theorems, Zaremba problem.

MSC: Primary 35J25; Secondary 35A01, 35A02, 35B45

Received: 10.12.2023 and 07.08.2024

DOI: 10.4213/sm10045

 English version: Sbornik: Mathematics, 2025, 216:8, 1021–1036

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