On the regularity theory for mixed local and nonlocal quasilinear parabolic equations
Analysis of PDEs
2021-10-07 v3
Abstract
We consider mixed local and nonlocal quasilinear parabolic equations of -Laplace type and discuss several regularity properties of weak solutions for such equations. More precisely, we establish local boundeness of weak subsolutions, lower semicontinuity of weak supersolutions as well as upper semicontinuity of weak subsolutions. We also discuss the pointwise behavior of the semicontinuous representatives. Our main results are valid for sign changing solutions. Our approach is purely analytic and is based on energy estimates and the De Giorgi theory.
Keywords
Cite
@article{arxiv.2108.02986,
title = {On the regularity theory for mixed local and nonlocal quasilinear parabolic equations},
author = {Prashanta Garain and Juha Kinnunen},
journal= {arXiv preprint arXiv:2108.02986},
year = {2021}
}