The Boyarsky–Meyers Inequality for the Zaremba Problem for p(∙)-Laplacian

Alkhutov Y.A. Chechkin G.A.
August 2023 Springer

Journal of Mathematical Sciences (United States)
2023 #274 Issue 4 423 - 440 pp.

We study the higher integrability of solutions to the Zaremba problem for the p(∙)-Laplacian in a plane domain with Lipschitz boundary. We prove that the Boyarsky–Meyers estimates for solutions are valid under a special ratio between the parts of the Dirichlet and Neumann conditions on the boundary.

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A. G. and N. G. Stoletov Vladimir State University, 87, Gor’kogo St, Vladimir, 600000, Russian Federation
Lomonosov Moscow State University, 1 Leninskie Gory, Moscow, 119991, Russian Federation
Institute of Mathematics with Computing Center, 112 Chernyshevskogo St., Ufa, 450008, Russian Federation
Institute of Mathematics and Mathematical, Modeling MES RK, 125, Pushkina St, Almaty, 050010, Kazakhstan

A. G. and N. G. Stoletov Vladimir State University
Lomonosov Moscow State University
Institute of Mathematics with Computing Center
Institute of Mathematics and Mathematical

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