Yu. A. Alkhutov, G. A. Chechkin, “Multidimensional Zaremba problem for the <nobr>$p(\,\cdot\,)$</nobr>-laplace equation. A Boyarsky–Meyers estimate”, TMF, 2024, Volume 218, Number 1,Pages <nobr>3

This article is cited in 3 papers

Multidimensional Zaremba problem for the $p(\,\cdot\,)$-laplace equation. A Boyarsky–Meyers estimate

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

^a Vladimir State University named after Alexander and Nikolay Stoletov, Vladimir, Russia
^b Institute of Mathematics and Mathematical Modeling, Ministry of Education and Science, Republic of Kazakhstan, Almaty, Kazakhstaт
^c Lomonosov Moscow State University, Moscow, Russia
^d Institute of Mathematics with Computing Center, Ufa Federal Research Centre, Russian Academy of Sciences, Ufa, Russia

Abstract: We prove the higher integrability of the gradient of solutions of the Zaremba problem in a bounded strongly Lipschitz domain for an inhomogeneous $p(\,\cdot\,)$-Laplace equation with a variable exponent $p$ having a logarithmic continuity modulus.

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

Received: 24.04.2023
Revised: 12.05.2023

DOI: 10.4213/tmf10522