Extrapolation for the $L^p$ Dirichlet Problem in Lipschitz domains

Zhongwei Shen

doi:https://doi.org/10.48550/arxiv.1801.00828

Extrapolation for the $L^p$ Dirichlet Problem in Lipschitz domains

Zhongwei Shen · arXiv (Cornell University) · 2018

Let $\mathcal{L}$ be a second-order linear elliptic operator with complex coefficients. We show that if the $L^p$ Dirichlet problem for the elliptic system $\mathcal{L}(u)=0$ in a fixed Lipschitz domain $Ω$ in $\mathbb{R}^d$ is solvable for some $1

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