A note on a critical problem with natural growth in the gradient

• Autores: Boumediene Abdellaoui, Ireneo Peral
• Localización: Journal of the European Mathematical Society, ISSN 1435-9855, Vol. 8, Nº 2, 2006, págs. 157-170
• Idioma: inglés
• DOI: 10.4171/jems/43
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• Resumen

  • 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.