Calculus of Variations and Geometric Measure Theory

Q. H. Nguyen - M. F. Bidaut-Véron - L. Véron

Quasilinear elliptic equations with a source reaction term involving the function and its gradient and measure data

created by nguyen on 04 May 2018


Submitted Paper

Inserted: 4 may 2018
Last Updated: 4 may 2018

Year: 2018

ArXiv: 1804.09419 PDF


We study the equation $-div(A(x,\nabla u))=g(x,u,\nabla u)+\mu$ where $\mu$ is a measure and either $g(x,u,\nabla u)\sim
\nabla u
^{q_2}$ or $g(x,u,\nabla u)\sim
\nabla u
^{s_2}$. We give sufficient conditions for existence of solutions expressed in terms of the Wolff potentials 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.