Year: 2009
Type: preprint
Abstract: The de Giorgi theory for minimal surfaces consists in studying sets whose indicator function is a (local) minimum of the BV norm. In this paper we replace the BV norm by the $H^σ$ norm, with $σ<1/2$, and try to understand what the minimisers look like. Parallel to the de Giorgi theory we prove that, if the boundary of a minimiser is sufficiently flat in the unit ball, then it is a smooth piece of hypersurface.
Source: arXiv (Cornell University)
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2950060297