Abstract

We consider the mixed Dirichlet-conormal problem on irregular domains in Two types of regularity results will be discussed: the regularity and a non-tangential maximal function estimate. The domain is assumed to be Reifenberg-flat, and the interfacial boundary is either Reifenberg-flat of co-dimension 2 or is locally sufficiently close to a Lipschitz function of m variables, where For the non-tangential maximal function estimate, we also require the domain to be Lipschitz.

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