The meyers estimates for domains perforated along the boundary
Chechkin G.A.
December-1 2021MDPI
Mathematics
2021#9Issue 23
In this paper, we consider an elliptic problem in a domain perforated along the boundary. By setting a homogeneous Dirichlet condition on the boundary of the cavities and a homogeneous Neumann condition on the outer boundary of the domain, we prove higher integrability of the gradient of the solution to the problem.
Higher integrability , Meyers estimates , Perforated domain , Small parameter
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Department of Differential Equations, Faculty of Mechanics and Mathematics, M.V. Lomonosov Moscow State University, Leninskie Gory, 1, Moscow, 119991, Russian Federation
Institute of Mathematics with Computing Center, Subdivision of the Ufa Federal Research Center of Russian Academy of Science, Chernyshevskogo st., 112, Ufa, 450008, Russian Federation
Institute of Mathematics and Mathematical Modeling, Pushkin st. 125, Almaty, 050010, Kazakhstan
Department of Differential Equations
Institute of Mathematics with Computing Center
Institute of Mathematics and Mathematical Modeling
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