On Higher Integrability of the Gradient of a Solution to the Zaremba Problem for p(.)-Laplace Equation in a Plane Domain

Alkhutov Y.A. Chechkin G.A.
August 2023 Pleiades Publishing

Lobachevskii Journal of Mathematics
2023 #44 Issue 8 3197 - 3206 pp.

Abstract: A higher integrability of the gradient of a solution to theZaremba problem in a bounded Lipschitz plane domain is proved forthe inhomogeneous p(.)-Laplace equation.

capacity , higher integrability , imbedding theorems , Meyers estimates , Zaremba problem

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A. G. and N. G. Stoletov Vladimir State University, Vladimir, 600000, Russian Federation
Moscow State University, Moscow, 119991, Russian Federation
Institute of Mathematics with Computing Center, Subdivision of the Ufa Federal Research Center of the Russian Academy of Science, Ufa, Russian Federation
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

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

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