JournalsjemsVol. 13 , No. 1DOI 10.4171/jems/242

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

  • Guy Barles

    Université de Tours, France
  • Emmanuel Chasseigne

    Université François Rabelais, Tours, France
  • Cyril Imbert

    Université Paris-Est Créteil Val de Marne, France
Hölder continuity of solutions of second-order non-linear elliptic integro-differential equations cover

Abstract

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.