A note on a critical problem with natural growth in the gradient
Ireneo Peral
Universidad Autónoma de Madrid, SpainBoumediene Abdellaoui
Université Aboubekr Belkaïd, Tlemcen, Algeria

Abstract
The paper analyzes the influence on the meaning of natural growth in the gradient, of a perturbation by a Hardy potential in some elliptic equations. We obtain a linear differential operator that, in a natural way, is the corresponding gradient for the perturbed elliptic problem.
The main results are: i) Optimal summability of the data to have weak solutions; ii) Optimal linear operator associated, and, iii) Multiplicity and characterization of all solutions in terms of some measures. The results also are new for the Laplace operator perturbed for an inverse-square potential.
Cite this article
Ireneo Peral, Boumediene Abdellaoui, A note on a critical problem with natural growth in the gradient. J. Eur. Math. Soc. 8 (2006), no. 2, pp. 157–170
DOI 10.4171/JEMS/43