Local regularity for fractional heat equations

Umberto Biccari; Mahamadi Warma; Enrique Zuazua

Local regularity for fractional heat equations

Analysis of PDEs 2017-05-23 v2

Authors: Umberto Biccari , Mahamadi Warma , Enrique Zuazua

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.

Keywords

regularity for elliptic equations regularity of solutions fractional laplacian

Cite

@article{arxiv.1704.07562,
  title  = {Local regularity for fractional heat equations},
  author = {Umberto Biccari and Mahamadi Warma and Enrique Zuazua},
  journal= {arXiv preprint arXiv:1704.07562},
  year   = {2017}
}

Comments

arXiv admin note: substantial text overlap with arXiv:1704.07560

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