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

Guy Barles, Shigeaki Koike, Olivier Ley, Erwin Topp*

*この研究の対応する著者

研究成果: Article査読

16 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)539-572
ページ数34
ジャーナルCalculus of Variations and Partial Differential Equations
54
1
DOI
出版ステータスPublished - 2015 9月 20
外部発表はい

ASJC Scopus subject areas

  • 分析
  • 応用数学

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