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

Barles, Guy, Chasseigne, Emmanuel, and Imbert, Cyril. "Hölder continuity of solutions of second-order non-linear elliptic integro-differential equations." Journal of the European Mathematical Society 013.1 (2011): 1-26. <http://eudml.org/doc/277808>.

@article{Barles2011,
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.},
author = {Barles, Guy, Chasseigne, Emmanuel, Imbert, Cyril},
journal = {Journal of the European Mathematical Society},
keywords = {Hölder regularity; integro-differential equations; Lévy operators; general non-local operators; viscosity solutions; integro-differential equations; degenerate elliptic functions; general non-local operators; viscosity solutions; Lévy operators; Hölder regularity},
language = {eng},
number = {1},
pages = {1-26},
publisher = {European Mathematical Society Publishing House},
title = {Hölder continuity of solutions of second-order non-linear elliptic integro-differential equations},
url = {http://eudml.org/doc/277808},
volume = {013},
year = {2011},
}

TY - JOUR
AU - Barles, Guy
AU - Chasseigne, Emmanuel
AU - Imbert, Cyril
TI - Hölder continuity of solutions of second-order non-linear elliptic integro-differential equations
JO - Journal of the European Mathematical Society
PY - 2011
PB - European Mathematical Society Publishing House
VL - 013
IS - 1
SP - 1
EP - 26
AB - 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.
LA - eng
KW - Hölder regularity; integro-differential equations; Lévy operators; general non-local operators; viscosity solutions; integro-differential equations; degenerate elliptic functions; general non-local operators; viscosity solutions; Lévy operators; Hölder regularity
UR - http://eudml.org/doc/277808
ER -