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Local elliptic regularity for the Dirichlet fractional Laplacian. (arXiv:1704.07560v1 [math.AP])
来源于:arXiv
We prove the $W^{2s,p}_{\textrm{loc}}$ local elliptic regularity of weak
solutions to the Dirichlet problem associated with the fractional Laplacian on
an arbitrary bounded open set of $\mathbb{R}^N$. The key tool consists in
analyzing carefully the elliptic equation satisfied by the solution locally,
after cut-off, to later employ sharp regularity results in the whole space. We
do it by two different methods. First working directly in the variational
formulation of the elliptic problem and then employing the heat kernel
representation of solutions. 查看全文>>