publication . Article . Preprint . 2012

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

Begoña Barrios; Alessio Figalli; Enrico Valdinoci;
Open Access
  • Published: 21 Feb 2012
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.
Subjects
free text keywords: Mathematics - Analysis of PDEs
Related Organizations
Funded by
NSF| Analytical and geometrical problems in calculus of variations and partial differential equations
Project
Analytical and geometrical problems in calculus of variations and partial differential equations
  • Funder: National Science Foundation (NSF)
  • Project Code: 0969962
  • Funding stream: Directorate for Mathematical & Physical Sciences | Division of Mathematical Sciences
, EC| EPSILON
Project
EPSILON
Elliptic Pdes and Symmetry of Interfaces and Layers for Odd Nonlinearities
  • Funder: European Commission (EC)
  • Project Code: 277749
  • Funding stream: FP7 | SP2 | ERC
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Preprint . 2012
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19 references, page 1 of 2
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