Quasilinear elliptic equations with a source reaction term involving the function and its gradient and measure data
Analysis of PDEs
2020-03-23 v2
Abstract
We study the equation --div(A(x, u)) = g(x, u, u) + where is a measure and either g(x, u, u) |u| q 1 u||u| q 2 or g(x, u, u) |u| s 1 u + ||u| s 2. We give sufficient conditions for existence of solutions expressed in terms of the Wolff potential or the Riesz potentials of the measure. Finally we connect the potential estimates on the measure with Lipchitz estimates with respect to some Bessel or Riesz capacity.
Cite
@article{arxiv.1804.09419,
title = {Quasilinear elliptic equations with a source reaction term involving the function and its gradient and measure data},
author = {Marie-Françoise Bidaut-Véron and Quoc-Hung Nguyen and Laurent Veron},
journal= {arXiv preprint arXiv:1804.09419},
year = {2020}
}