ON ZAREMBA PROBLEM FOR SECOND–ORDER LINEAR ELLIPTIC EQUATION WITH DRIFT IN CASE OF LIMIT EXPONENT
Aliyev M.D. Alkhutov Yu.A. Chechkin G.A.
2024Institute of Mathematics with Computing Centre
Ufa Mathematical Journal
2024#16Issue 41 - 11 pp.
We establish the unique solvability of the Zaremba problem with the homogeneous Dirichlet and Neumann boundary conditions for an inhomogeneous linear second order second order equation in the divergence form with measurable coefficients and lower order terms. The problem is considered in a bounded strictly Lipschitz domain. We suppose that the domain is contained in an η–dimensional Euclidean space, where η ≽ 2. If η > 2, then the lower coefficient belong to the Lebesgue space with the limiting summability exponent from the Sobolev embedding theorem. If η = 2, then the lower coefficients are summable at each power exceeding two. Apart of the unique solvability, we establish an energy estimate for the solution.
capacity , drift , limiting exponent , solvability , Zaremba problem
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Baku State University, Academic Zahid Khalilov str. 33, Baku, AZ1148, Azerbaijan
Vladimir State University named after Alexander and Nikolay Stoletovs, Stroiteley av. 11, Vladimir, 600000, Russian Federation
Lomonosov Moscow State University, Leninskie Gory 1, Moscow, 119991, Russian Federation
Institute of Mathematics, Ufa Federal Research Center, RAS, Chernyshevsky str. 112, Ufa, 450008, Russian Federation
Institute of Mathematics and Mathematical Modeling, Pushkin str. 125, Almaty, 05010, Kazakhstan
Baku State University
Vladimir State University named after Alexander and Nikolay Stoletovs
Lomonosov Moscow State University
Institute of Mathematics
Institute of Mathematics and Mathematical Modeling
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