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

• Begoña Barrios ^[1] ; Alessio Figalli ^[2] ; Enrico Valdinoci ^[3]
  1. [1] Universidad Autónoma de Madrid

     Universidad Autónoma de Madrid

     Madrid, España

     
  2. [2] University of Texas at Austin

     University of Texas at Austin

     Estados Unidos

     
  3. [3] Weierstrass Institute for Applied Analysis and Stochastics

     Weierstrass Institute for Applied Analysis and Stochastics

     Berlin, Stadt, Alemania

     

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• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 13, Nº 3, 2014, págs. 609-639
• Idioma: inglés
• DOI: 10.2422/2036-2145.201202_007
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• Resumen

  • We prove that C1,↵ s-minimal surfaces are of class C1. 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.