Estimates for the $L^q$-mixed problem in $C^{1,1}$-domains

Abstract

We consider the $L^q$-mixed problem in domains in ${\mathbf{R}}^n$ with $C^{1,1}$-boundary. We assume that the boundary between the sets where we specify Neumann and Dirichlet data is Lipschitz. With these assumptions, we show that we may solve the $L^q$-mixed problem for $q$ in the range $1<q<n/(n-1)$.

15 pages

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