authors
- PABLO MARTINEZ, ARTURO DE
- QUIRÓS, FERNANDO
- RODRIGUEZ, ANA
Regularity theory for singular nonlocal diffusion equations
Articles
Overview
published in
publication date
- October 2018
volume
- 57:136
Digital Object Identifier (DOI)
International Standard Serial Number (ISSN)
- 0944-2669
Electronic International Standard Serial Number (EISSN)
- 1432-0835
abstract
- We prove continuity for bounded weak solutions of a nonlinear nonlocal parabolic type equation associated to a Dirichlet form with a rough kernel. The equation is allowed to be singular at the level zero, and solutions may change sign. If the nonlinearity in the equation does not oscillate too much at the origin, the solution is proved to be moreover Holder continuous. The results are new even when the Dirichlet form is the one corresponding to the fractional Laplacian.