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

2012/02/21 by Begoña Barrios Barrera, Alessio Figalli, Barrera, Begoña Barrios +3 · 2 citations
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1202.4606

openalex publication_date 2012/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that C^1,\α s-minimal surfaces are automatically\nC^\∞. For this, we develop a new bootstrap regularity theory for\nsolutions of integro-differential equations of very general type, which we\nbelieve is of independent interest.\n

Citations

• Hitchhikerʼs guide to the fractional Sobolev spaces
• Non-local gradient dependent operators
• The Evans-Krylov theorem for nonlocal fully nonlinear equations
• Regularity of the obstacle problem for a fractional power of the laplace operator
• The Evans-Krylov theorem for non local fully non linear equations

Cited by

• Gamma-convergence as s→1^- of anisotropic nonlocal fractional perimeter functionals
• Gamma-convergence of nonlocal energies for partitions

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• Obstacle problems for integro-differential operators: Higher regularity of free boundaries
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• Partial regularity in nonlocal systems I
• A lemma on the minimal surfaces