Remarks on the maximum principle for nonlinear elliptic PDEs with quadratic growth conditions

• Guy Barles ^[1] ; Alain-Philippe Blanc ^[1] ; Christine Georgelin ^[1] ; Magdalena Kobylanski ^[1]
  1. [1] Université de Tours, France
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 28, Nº 3, 1999, págs. 381-404
• Idioma: inglés
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• Resumen

  • In this article, we prove that the maximum principle holds for nonlinear second-order elliptic equations with quadratic growth conditions under general asumptions. We extend the results recently obtained by Fr. Murat and the first author by allowing a more general dependence in x in the growth condition, namely an L N -dependence instead of a L ∞ one. Our framework is close to the recent existence results of Fr. Murat and V. Ferone and we provide the uniqueness of their solutions under slightly less general conditions. Our proofs consist in mixing the classical linear arguments of the weak maximum principle given in the book of Gilbarg and Trudinger with the nonlinear ones of G. Barles and Fr. Murat.