Abstract
We study the problem of solvability of the Dirichlet problem for second-order linear and quasilinear uniformly elliptic equations in a bounded domain whose boundary contains a conical point. We prove new theorems on the unique solvability of a linear problem under minimal smoothness conditions for the coefficients, right-hand sides, and the boundary of the domain. We find classes of solvability of the problem for quasilinear equations under natural conditions.
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Borsuk, M.V. On the solvability of the dirichlet problem for elliptic nondivergent equations of the second order in a domain with conical point. Ukr Math J 48, 13–26 (1996). https://doi.org/10.1007/BF02390979
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DOI: https://doi.org/10.1007/BF02390979