Gradient estimates of very weak solutions to general quasilinear elliptic equations
Analysis of PDEs
2022-02-14 v1
Abstract
We establish a gradient estimate for a very weak solution to a quasilinear elliptic equation with a nonstandard growth condition, which is a natural generalization of the -Laplace equation. We investigate the maximum extent for the gradient estimate to hold without imposing any regularity assumption on the nonlinearity other than basic structure assumptions. Our results also include a higher integrability result of the gradient and the existence for the very weak solutions to such nonlinear problems.
Keywords
Cite
@article{arxiv.2202.05414,
title = {Gradient estimates of very weak solutions to general quasilinear elliptic equations},
author = {Sun-Sig Byun and Minkyu Lim},
journal= {arXiv preprint arXiv:2202.05414},
year = {2022}
}