Regularity results and large time behavior for integro-differential equations with coercive Hamiltonians

Guy Barles, Shigeaki Koike, Olivier Ley, Erwin Topp

Research output: Contribution to journalArticle

11 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)539-572
Number of pages34
JournalCalculus of Variations and Partial Differential Equations
Volume54
Issue number1
DOIs
Publication statusPublished - 2015 Sep 20
Externally publishedYes

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Hamiltonians
Maximum principle
Integrodifferential equations
Large Time Behavior
Linearization
Integro-differential Equation
Regularity
Subsolution
Strong Maximum Principle
Gradient Term
Supersolution
Evolution Problems
A Priori Estimates
Elliptic Equations
Lipschitz
Asymptotic Behavior
Necessary
Estimate

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Regularity results and large time behavior for integro-differential equations with coercive Hamiltonians. / Barles, Guy; Koike, Shigeaki; Ley, Olivier; Topp, Erwin.

In: Calculus of Variations and Partial Differential Equations, Vol. 54, No. 1, 20.09.2015, p. 539-572.

Research output: Contribution to journalArticle

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