Yu. A. Alkhutov, G. A. Chechkin, “Increased integrability of the gradient of the solution to the Zaremba problem for the Poisson equation”, Dokl. RAN. Math. Inf. Proc. Upr., 2021, Volume 497,Pages <nobr>3

This article is cited in 19 papers

MATHEMATICS

Increased integrability of the gradient of the solution to the Zaremba problem for the Poisson equation

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

^a Vladimir State University, Vladimir, Russia
^b Lomonosov Moscow State University, Moscow, Russia
^c Institute of Mathematics with Computing Center, Ufa Federal Research Center, Russian Academy of Science, Ufa, Bashkortostan, Russia
^d Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

Abstract: An estimate is obtained for the increased integrability of the gradient of the solution to the Zaremba problem in a bounded plane domain with a Lipschitz boundary and rapidly alternating Dirichlet and Neumann boundary conditions, with an increased integrability exponent independent of the frequency of the boundary condition change.

Keywords: Meyers estimates, embedding theorems, rapidly changing type of boundary conditions.

UDC: 517.954; 517.982

Presented: V. V. Kozlov
Received: 18.02.2021
Revised: 18.02.2021
Accepted: 24.02.2021

DOI: 10.31857/S2686954321020028