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

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Barrera, Begoña Barrios; Figalli, Alessio; Valdinoci, Enrico;
(2012)
  • Subject: Mathematics - Analysis of PDEs

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 (19)
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