Unité Mixte de Recherche du C.N.R.S. N°7534

Abstract : In this paper we deal with existence and uniqueness of solution to super-linear problems for the Pucci operator: $$\,-\M^+(D^2u)+|u|^{s-1}u=f(x)\,\quad \mbox{in } \RR^n,$$ where $s>1$ and $f$ satisfies only local integrability conditions. This result is well known when, instead of the Pucci operator, the Laplacian or a divergence form operator is considered. Our existence results use the Alexandroff-Bakelman-Pucci inequality since we cannot use any variational formulation. For radially symmetric $f$ we can prove our results under less local integrability assumptions, taking advantage of an appropriate variational formulation. We also obtain an existence result with boundary explosion in smooth domains.

 Pucci operator, super-linear elliptic problem, boundary explosion, local data.
 ESTEBAN Maria J., FELMER Patricio, QUAAS A.
2007-51
09-12-2007

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