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arXiv · 1904.00545

Optimal regularity for a Dirichlet-conormal problem in Reifenberg flat domain

Jongkeun Choi·Hongjie Dong·Zongyuan Li
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Abstract

We study the divergence form second-order elliptic equations with mixed Dirichlet-conormal boundary conditions. The unique $W^{1,p}$ 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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Jongkeun Choi, Hongjie Dong, Zongyuan Li. 2019-04-01. Optimal regularity for a Dirichlet-conormal problem in Reifenberg flat domain. https://arxiv.org/abs/1904.00545

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