Regularity properties of nonlocal minimal surfaces via limiting arguments

Details Regularity properties of nonlocal minimal surfaces via limiting arguments Regularity properties of nonlocal minimal surfaces via limiting arguments

2011-05-05

arxiv.org/abs/1105.1158v1

Mathematics

Analysis of PDEs

Scientific paper

We prove an improvement of flatness result for nonlocal minimal surfaces
which is independent of the fractional parameter $s$ when $s\rightarrow 1^-$.
As a consequence, we obtain that all the nonlocal minimal cones are flat and
that all the nonlocal minimal surfaces are smooth when the dimension of the
ambient space is less or equal than 7 and $s$ is close to 1.

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