Boyarsky–Meyers Estimate for Solutions to Zaremba Problem
Alkhutov Y.A. Chechkin G.A. Maz’ya V.G.
August 2022Springer Science and Business Media Deutschland GmbH
Archive for Rational Mechanics and Analysis
2022#245Issue 21197 - 1211 pp.
The variational solution to the Zaremba problem for a divergent linear second order elliptic equation with measurable coefficients is considered. The problem is set in a local Lipschitz graph domain. An estimate in L2+δ, δ> 0 , for the gradient of a solution, is proved. An example of the problem with the Dirichlet data supported by a fractal set of zero (n- 1) -dimensional measure and non-zero p-capacity, p> 1 is constructed.
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A.G. and N.G. Stoletov Vladimir State University, Stroitelej st., 11, Vladimir, Russian Federation
M.V. Lomonosov Moscow State University, Leninskie gory, 1, Moscow, Russian Federation
Institute of Mathematics with Computing Center - Subdivision of the Ufa Federal Research Center of Russian Academy of Science, Ufa, Russian Federation
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Linköpings Universitet, Linköping, Sweden
RUDN University, Miklukho-Maklaya St, 6, Moscow, Russian Federation
A.G. and N.G. Stoletov Vladimir State University
M.V. Lomonosov Moscow State University
Institute of Mathematics with Computing Center - Subdivision of the Ufa Federal Research Center of Russian Academy of Science
Institute of Mathematics and Mathematical Modeling
Linköpings Universitet
RUDN University
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