On boundaryvalue problems in domains without (A)-condition
DOI:
https://doi.org/10.15407/dopovidi2019.03.017Keywords:
and Poincaré boundaryvalue problems, angular limits, Beltrami equations, Dirichlet, Hilbert, logarithmic capacity, Neumann, quasiconformal functions, quasihyperbolic boundary conditionAbstract
We study the Hilbert boundaryvalue problem for the Beltrami equations in the Jordan domains satisfying the quasihyperbolic boundary condition by Gehring—Martio, generally speaking, without the standard (A)-condition by Ladyzhenskaya—Ural'tseva. Assuming that the coefficients of the problem are functions of countable bounded variation and the boundary data are measurable with respect to the logarithmic capacity, we prove the existence of its solutions. As consequences, we derive the existence of nonclassical solutions of the Dirichlet, Neumann and Poincaré boundaryvalue problems for generalizations of the Laplace equation in anisotropic and inhomogeneous media.
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