Local regularity for fractional heat equations

U. Biccari, M. Warna, E. Zuazua Local regularity for fractional heat equations, DOI: 10.1007/978-3-319-97613-6 Recent Advances in PDEs: Analysis, Numerics and Control, SEMA SIMAI Springer Series, Volume 17 (2018)

Abstract: 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 $\Omega\subset\mathbb{R}^N$. Proofs combine classical abstract regularity results for parabolic equations with some new local regularity results for the associated elliptic problems.

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