Lipschitz regularity for integro-differential equations with coercive Hamiltonians and application to large time behavior

Abstract : In this paper, we provide suitable adaptations of the " weak version of Bernstein method " introduced by the first author in 1991, in order to obtain Lipschitz regularity results and Lipschitz estimates for nonlinear integro-differential elliptic and parabolic equations set in the whole space. Our interest is to obtain such Lipschitz results to possibly degenerate equations, or to equations which are indeed " uniformly el-liptic " (maybe in the nonlocal sense) but which do not satisfy the usual " growth condition " on the gradient term allowing to use (for example) the Ishii-Lions' method. We treat the case of a model equation with a superlinear coercivity on the gradient term which has a leading role in the equation. This regularity result together with comparison principle provided for the problem allow to obtain the ergodic large time behavior of the evolution problem in the periodic setting.
Document type :
Journal articles
Complete list of metadatas

Cited literature [36 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01278603
Contributor : Olivier Ley <>
Submitted on : Wednesday, February 24, 2016 - 3:32:59 PM
Last modification on : Thursday, February 7, 2019 - 4:12:07 PM
Long-term archiving on : Wednesday, May 25, 2016 - 10:37:41 AM

Files

lipschitz_Bernstein.pdf
Files produced by the author(s)

Identifiers

Citation

Guy Barles, Olivier Ley, Erwin Topp. Lipschitz regularity for integro-differential equations with coercive Hamiltonians and application to large time behavior. Nonlinearity, IOP Publishing, 2017, 30 (2), pp.703-734. ⟨10.1088/1361-6544/aa527f⟩. ⟨hal-01278603⟩

Share

Metrics

Record views

546

Files downloads

257