The Meyers Estimates for Domains Perforated along the Boundary

Gregory A. Chechkin
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Gregory A. Chechkin: Department of Differential Equations, Faculty of Mechanics and Mathematics, M.V. Lomonosov Moscow State University, Leninskie Gory, 1, 119991 Moscow, Russia

Mathematics, 2021, vol. 9, issue 23, 1-11

Abstract: 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.

Keywords: higher integrability; Meyers estimates; perforated domain; small parameter (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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