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

2018/04/25 by Bidaut-Véron, Marie-Françoise, Nguyen, Quoc-Hung, Veron, Laurent
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1804.09419

Abstract

We study the equation --div(A(x, u)) = g(x, u, u) + μ where μ 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.

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