Calculus of Variations and Geometric Measure Theory

C. Bjorland - L. Caffarelli - A. Figalli

Non-Local Gradient Dependent Operators

created by figalli on 28 Mar 2012


Accepted Paper

Inserted: 28 mar 2012
Last Updated: 28 mar 2012

Journal: Adv. Math.
Year: 2012


In this paper we study a general class of ``quasilinear non-local equations'' depending on the gradient which arise from tug-of-war games. We establish a $C^\alpha$-$C^{1,\alpha}$-$C^{2,\alpha}$ regularity theory for these equations (the kind of regularity depending on the assumptions on the kernel), and we construct different non-local approximations of the $p$-Laplacian.