Submitted Paper

Inserted: 4 may 2018
Last Updated: 4 may 2018

Year: 2018

Abstract:

We study the equation $-div(A(x,\nabla u))=g(x,u,\nabla u)+\mu$ where $\mu$ is a measure and either $g(x,u,\nabla u)\sim
u
^{q_1}u
\nabla u
^{q_2}$ or $g(x,u,\nabla u)\sim
u
^{s_1}u+
\nabla u
^{s_2}$. 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.