Repositorio Institucional Examinando por Autor "Warma, Mahamadi"

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Addendum: Local elliptic regularity for the Dirichlet fractional Laplacian
(Walter de Gruyter GmbH, 2017) Biccari, Umberto; Warma, Mahamadi; Zuazua, Enrique
In [1], for 1 < p < 1
Local elliptic regularity for the Dirichlet fractional Laplacian
(Walter de Gruyter GmbH, 2017) Biccari, Umberto; Warma, Mahamadi; Zuazua, Enrique
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.
Local regularity for fractional heat equations
(Springer International Publishing, 2018) Biccari, Umberto; Warma, Mahamadi; Zuazua, Enrique
We prove the maximal local regularity of weak solutions to the parabolic problem associated with the fractional Laplacian with homogeneous Dirichlet boundary conditions on an arbitrary bounded open set Ω ⊂ ℝN. Proofs combine classical abstract regularity results for parabolic equations with some new local regularity results for the associated elliptic problems.