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 Cet article a éte moissonné depuis la source EMS Press

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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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     author = {Guy Barles and Emmanuel Chasseigne and Cyril Imbert},
     title = {H\"older continuity of solutions of second-order non-linear elliptic integro-differential equations},
     journal = {Journal of the European Mathematical Society},
     pages = {1--26},
     year = {2011},
     volume = {13},
     number = {1},
     doi = {10.4171/jems/242},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/242/}
}
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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

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