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

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

2012-02-21

arxiv.org/abs/1202.4606v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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