hal-00608848, version 2
Lipschitz Regularity of Solutions for Mixed Integro-Differential Equations
(15/07/2011)
Résumé : We establish new Hoelder and Lipschitz estimates for viscosity solutions of a large class of elliptic and parabolic nonlinear integro-differential equations, by the classical Ishii-Lions's method. We thus extend the Hoelder regularity results recently obtained by Barles, Chasseigne and Imbert (2011). In addition, we deal with a new class of nonlocal equations that we term mixed integro-differential equations. These equations are particularly interesting, as they are degenerate both in the local and nonlocal term, but their overall behavior is driven by the local-nonlocal interaction, e.g. the fractional diffusion may give the ellipticity in one direction and the classical diffusion in the complementary one.
- 1 :
- CNRS : UMR6083 – Université François Rabelais - Tours
- 2 :
- CNRS : UMR8536 – École normale supérieure de Cachan - ENS Cachan
- 3 :
- CNRS : UMR7534 – Université Paris IX - Paris Dauphine
- 4 :
- CNRS : UMR8553 – Ecole normale supérieure de Paris - ENS Paris
- Domaine : Mathématiques/Equations aux dérivées partielles
- Mots-clés : regularity of generalized solutions – viscosity solutions – nonlinear elliptic equations integro partial-differential equations
- Versions disponibles : v1 (16-07-2011) v2 (06-01-2012)
- hal-00608848, version 2
- http://hal.archives-ouvertes.fr/hal-00608848
- oai:hal.archives-ouvertes.fr:hal-00608848
- Contributeur :
- Soumis le : Jeudi 5 Janvier 2012, 22:48:07
- Dernière modification le : Vendredi 6 Janvier 2012, 09:36:24
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