On Higher Integrability of Solutions to the Poisson Equation with Drift in Domains Perforated Along the Boundary
Chechkin G.A. Chechkina T.P.
September 2024Pleiades Publishing
Russian Journal of Mathematical Physics
2024#31Issue 3407 - 417 pp.
Abstract: In the paper, we consider a linear second order elliptic problem with drift in a domain perforated along the boundary. Setting homogeneous Dirichlet condition on the boundary of the cavities and homogeneous Neumann condition on the outer boundary of the domain, we prove the higher integrability of the gradient of the solution to the problem (the Boyarsky–Meyers estimate). DOI 10.1134/S1061920824030051
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Department of Differential Equations, Faculty of Mechanics and Mathematics, M. V. Lomonosov Moscow State University, Moscow, 119991, Russian Federation
Institute of Mathematics with Computing Center, Subdivision of the Ufa Federal Research Center of Russian Academy of Science, Ufa, 450008, Russian Federation
Institute of Mathematics and Mathematical Modeling, Ministry of Education and Science, Almaty, 050010, Kazakhstan
Department of Mathematics, National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Moscow, 115409, Russian Federation
Department of Differential Equations
Institute of Mathematics with Computing Center
Institute of Mathematics and Mathematical Modeling
Department of Mathematics
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