Existence of $C^\alpha$ solutions to integro-PDEs

Chenchen Mou

Existence of $C^\alpha$ solutions to integro-PDEs

Analysis of PDEs 2018-09-14 v3

Authors: Chenchen Mou

Abstract

This paper is concerned with existence of a $C^{\alpha}$ viscosity solution of a second order non-translation invariant integro-PDE. We first obtain a weak Harnack inequality for such integro-PDE. We then use the weak Harnack inequality to prove H\"older regularity and existence of solutions of the integro-PDEs.

Keywords

integro-pde viscosity solution weak harnack inequality holder regularity existence of solutions non-translation invariant

Cite

@article{arxiv.1801.01028,
  title  = {Existence of $C^\alpha$ solutions to integro-PDEs},
  author = {Chenchen Mou},
  journal= {arXiv preprint arXiv:1801.01028},
  year   = {2018}
}

Comments

References added, 28 pages

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