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- W2607197818 abstract "We analyze the local elliptic regularity of weak solutions to the Dirichlet problem associated with the fractional Laplacian $(-Delta)^s$ on an arbitrary bounded open set $Omegasubsetmathbb{R}^N$. For $1<p<2$, we obtain regularity in the Besov space $B^{2s}_{p,2,textrm{loc}}(Omega)$, while for $2leq p<infty$ we show that the solutions belong to $W^{2s,p}_{textrm{loc}}(Omega)$. 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." @default.
- W2607197818 created "2017-04-28" @default.
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- W2607197818 date "2017-04-25" @default.
- W2607197818 modified "2023-10-06" @default.
- W2607197818 title "Local elliptic regularity for the Dirichlet fractional Laplacian" @default.
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