2001-Luminy conference on Quasilinear Elliptic and Parabolic Equations and Systems,
Electron. J. Diff. Eqns., Conf. 08, 2002, pp. 23-34.

Necessary conditions of existence for an elliptic equation with source term and measure data involving p-Laplacian

Marie-Francoise Bidaut-Veron

Abstract:
We study the nonnegative solutions to equation
$$ -\Delta_{p}u=u^{q}+\lambda\nu, $$
in a bounded domain $\Omega$ of $\mathbb{R}^{N}$, where 1 less than p less than N, q greater than p-1, $\nu$ is a nonnegative Radon measure on $\Omega$, and $\lambda$ greater than 0 is a parameter. We give necessary conditions on $\nu$ for existence, with $\lambda$ small enough, in terms of capacity. We also give a priori estimates of the solutions.

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Marie-Francoise Bidaut-Veron
Laboratoire de Mathematiques et Physique Theorique
CNRS UMR 6083, Faculte des Sciences
Parc de Grandmont, 37200 Tours, France
e-mail: veronmf@univ-tours.fr

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