Regularity Results and Large Time Behavior for Integro-Differential Equations with Coercive Hamiltonians

Abstract : In this paper we obtain regularity results for elliptic integro-differential equations driven by the stronger effect of coercive gradient terms. This feature allows us to construct suitable strict supersolutions from which we conclude Hölder estimates for bounded subsolutions. In many interesting situations, this gives way to a priori estimates for subsolutions. We apply this regularity results to obtain the ergodic asymptotic behavior of the associated evolution problem in the case of superlinear equations. One of the surprising features in our proof is that it avoids the key ingredient which are usually necessary to use the Strong Maximum Principle: linearization based on the Lipschitz regularity of the solution of the ergodic problem. The proof entirely relies on the Hölder regularity.
Document type :
Journal articles
Complete list of metadatas

Cited literature [36 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00980228
Contributor : Guy Barles <>
Submitted on : Thursday, April 17, 2014 - 4:02:17 PM
Last modification on : Thursday, February 7, 2019 - 5:15:11 PM
Long-term archiving on : Monday, April 10, 2017 - 3:11:42 PM

Files

bklt-final.pdf
Files produced by the author(s)

Identifiers

Citation

Guy Barles, Shigeaki Koike, Olivier Ley, Erwin Topp. Regularity Results and Large Time Behavior for Integro-Differential Equations with Coercive Hamiltonians. Calculus of Variations and Partial Differential Equations, Springer Verlag, 2015, 54 (1), pp.535-572. ⟨10.1007/s00526-014-0794-x⟩. ⟨hal-00980228⟩

Share

Metrics

Record views

781

Files downloads

355