Calculus of Variations and Geometric Measure Theory

B. Barrios - A. Figalli - E. Valdinoci

Bootstrap regularity for integro-differential operators and its application to nonlocal minimal surfaces

created by figalli on 16 Aug 2012
modified on 14 Jul 2013


Accepted Paper

Inserted: 16 aug 2012
Last Updated: 14 jul 2013

Journal: Ann. Scuola Norm. Sup. Pisa Cl. Sci.
Year: 2012


We prove that $C^{1,\alpha}$ $s$-minimal surfaces are of class $C^\infty$. For this, we develop a new bootstrap regularity theory for solutions of integro-differential equations of very general type, which we believe is of independent interest.