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Pré-Publication, Document De Travail Année : 2007

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

Résumé

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.
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Dates et versions

hal-00179690 , version 1 (16-10-2007)
hal-00179690 , version 2 (03-09-2010)

Identifiants

  • HAL Id : hal-00179690 , version 1

Citer

Guy Barles, Emmanuel Chasseigne, Cyril Imbert. Hôlder continuity of solutions of second-order non-linear elliptic integro-differential equations. 2007. ⟨hal-00179690v1⟩
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