Multidimensional Zaremba problem for the p(.) -Laplace equation. A Boyarsky–Meyers estimate
Alkhutov Y.A. Chechkin G.A.
January 2024Pleiades Publishing
Theoretical and Mathematical Physics(Russian Federation)
2024#218Issue 11 - 18 pp.
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(.) -Laplace equation with a variable exponent p having a logarithmic continuity modulus.
capacity , embedding theorems , higher integrability , Meyers estimates , Zaremba problem
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Vladimir State University named after Alexander and Nikolay Stoletov, Vladimir, Russian Federation
Institute of Mathematics and Mathematical Modeling, Ministry of Education and Science Republic of Kazakhstan, Almaty, Kazakhstan
Lomonosov Moscow State University, Moscow, Russian Federation
Institute of Mathematics with Computing Center, Ufa Federal Research Center, Russian Academy of Sciences, Ufa, Russian Federation
Vladimir State University named after Alexander and Nikolay Stoletov
Institute of Mathematics and Mathematical Modeling
Lomonosov Moscow State University
Institute of Mathematics with Computing Center
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