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arXiv · 1902.08843

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

R. M. Brown·L. D. Croyle
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Abstract

We consider the $L^q$-mixed problem in domains in ${\bf R}^n$ 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 $1<q < n/(n-1)$.

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R. M. Brown, L. D. Croyle. 2019-02-23. Estimates for the $L^q$-mixed problem in $C^{1,1}$-domains. https://doi.org/10.1080/17476933.2019.1709971

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