Lipschitz regularity results for nonlinear strictly elliptic equations and applications

Abstract : Most of lipschitz regularity results for nonlinear strictly elliptic equations are obtained for a suitable growth power of the nonlinearity with respect to the gradient variable (subquadratic for instance). For equations with superquadratic growth power in gradient, one usually uses weak Bernstein-type arguments which require regularity and/or convex-type assumptions on the gradient nonlinearity. In this article, we obtain new Lipschitz regularity results for a large class of nonlinear strictly elliptic equations with possibly arbitrary growth power of the Hamiltonian with respect to the gradient variable using some ideas coming from Ishii-Lions' method. We use these bounds to solve an ergodic problem and to study the regularity and the large time behavior of the solution of the evolution equation.
Type de document :
Article dans une revue
Journal of Differential Equations, Elsevier, 2017, 263 (7), pp.4324-4354. 〈10.1016/j.jde.2017.05.020〉
Liste complète des métadonnées

Littérature citée [20 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-01344438
Contributeur : Olivier Ley <>
Soumis le : lundi 11 juillet 2016 - 21:17:41
Dernière modification le : jeudi 11 janvier 2018 - 06:12:25
Document(s) archivé(s) le : mercredi 12 octobre 2016 - 15:00:33

Fichiers

ln2016_lip-reg.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Citation

Olivier Ley, Vinh Duc Nguyen. Lipschitz regularity results for nonlinear strictly elliptic equations and applications. Journal of Differential Equations, Elsevier, 2017, 263 (7), pp.4324-4354. 〈10.1016/j.jde.2017.05.020〉. 〈hal-01344438〉

Partager

Métriques

Consultations de la notice

377

Téléchargements de fichiers

102