Yu. A. Alkhutov, G. A. Chechkin, “Boyarsky-Meyers estimate of solution to the Zaremba problem for Poisson's equation with drift”, Mat. Sb., 2025, Volume 216, Number 8,Pages <nobr>5

Boyarsky-Meyers estimate of solution to the Zaremba problem for Poisson's equation with drift

Yu. A. Alkhutov^a, G. A. Chechkin^bcd

^a 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 terms in a bounded domain with Lipschitz boundary and fast alternation of Dirichlet and Neumann conditions.

Keywords: Boyarsky-Meyers estimates, embedding theorems, Zaremba problems.

MSC: 35B05, 35J25

Received: 10.12.2023 and 07.08.2024

DOI: 10.4213/sm10045