Geodesic
Hölder continuity of solutions of second-order non-linear elliptic integro-differential equations
Journal of the European Mathematical Society, Tome 13 (2011) no. 1, pp. 1-26.

Voir la notice de l'article provenant de la source EMS Press

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.
DOI : 10.4171/jems/242
Classification : 35-XX, 00-XX
Keywords: Hölder regularity, integro-differential equations, Lévy operators, general non-local operators, viscosity solutions 
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Guy Barles; Emmanuel Chasseigne; Cyril Imbert. Hölder continuity of solutions of second-order non-linear elliptic integro-differential equations. Journal of the European Mathematical Society, Tome 13 (2011) no. 1, pp. 1-26. doi : 10.4171/jems/242. http://geodesic.mathdoc.fr/articles/10.4171/jems/242/

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