Continuity of solutions to a nonlinear fractional diffusion equation

Lorenzo Brasco; Erik Lindgren; Martin Strömqvist

Continuity of solutions to a nonlinear fractional diffusion equation

Analysis of PDEs 2019-07-02 v1

Authors: Lorenzo Brasco , Erik Lindgren , Martin Strömqvist

Abstract

We study a parabolic equation for the fractional $p-$ Laplacian of order $s$ , for $p\ge 2$ and $0<s<1$ . We provide space-time H\"older estimates for weak solutions, with explicit exponents. The proofs are based on iterated discrete differentiation of the equation in the spirit of J. Moser.

Keywords

fractional laplacian regularity of solutions fractional diffusion equations

Cite

@article{arxiv.1907.00910,
  title  = {Continuity of solutions to a nonlinear fractional diffusion equation},
  author = {Lorenzo Brasco and Erik Lindgren and Martin Strömqvist},
  journal= {arXiv preprint arXiv:1907.00910},
  year   = {2019}
}

Comments

45 pages

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