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NUMBER M19024
AUTHOR Choi, Jongkeun
TITLE Optimal Regularity for a Dirichlet-Conormal Problem in Reifenberg Flat Domain
ARCHIVE arXiv:1904.00545
FILE  
JOURNAL APPLIED MATHEMATICS AND OPTIMIZATION, 2021
ABSTRACT We study the divergence form second-order elliptic equations with mixed Dirichlet-conormal boundary conditions. The unique W1,p solvability is obtained with p being in the optimal range (4 / 3, 4). The leading coefficients are assumed to have small mean oscillations and the boundary of domain is Reifenberg flat. We also assume that the two boundary conditions are separated by some Reifenberg flat set of co-dimension 2 on the boundary.
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