Local elliptic regularity for the Dirichlet fractional Laplacian
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2017
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Walter de Gruyter GmbH
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We prove the Wloc2s,p local elliptic regularity of weak solutions to the Dirichlet problem associated with the fractional Laplacian on an arbitrary bounded open set of RN. 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.
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Biccari, U., Warma, M., & Zuazua, E. (2017). Local Elliptic Regularity for the Dirichlet Fractional Laplacian. Advanced Nonlinear Studies, 17(2), 387-409. https://doi.org/10.1515/ANS-2017-0014