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

Abstract

We prove that $C^{1,\alpha }$ $s$-minimal surfaces are automatically $C^{\infty }$. 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.

References in corpus (3)

• Regularity theory for fully nonlinear integro-differential equations
• Gamma-convergence of nonlocal perimeter functionals
• The Evans-Krylov theorem for non local fully non linear equations