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Hölder continuity of solutions of second-order non-linear elliptic integro-differential equations

Barles, Guy; Chasseigne, Emmanuel; Imbert, Cyril (2011), Hölder continuity of solutions of second-order non-linear elliptic integro-differential equations, Journal of the European Mathematical Society, 13, 1. http://dx.doi.org/10.4171/JEMS/242

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00179690/en/
Date
2011
Journal name
Journal of the European Mathematical Society
Volume
13
Number
1
Publisher
European Mathematical Society
Publication identifier
Metadata
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Author(s)
Barles, Guy
Chasseigne, Emmanuel
Imbert, Cyril cc
Abstract (EN)
This paper is concerned with the Hölder regularity of viscosity solutions of second-order, fully non-linear elliptic integro-differential equations. Our results rely on two key ingredients: first we assume that, at each point of the domain, either the equation is strictly elliptic in the classical fully non-linear sense, or (and this is the most original part of our work) the equation is strictly elliptic in a non-local non-linear sense we make precise. Next we impose some regularity and growth conditions on the equation. These results are concerned with a large class of integro-differential operators whose singular measures depend on x and also a large class of equations, including Bellman-Isaacs Equations.
Subjects / Keywords
Hölder regularity; integro-differential equations; Lévy operators; general non-local operators; viscosity solutions