# Minimization of anisotropic energies in classes of rectifiable varifolds

created by derosa on 24 Nov 2016
modified on 13 Feb 2019

[BibTeX]

Published Paper

Inserted: 24 nov 2016
Last Updated: 13 feb 2019

Journal: SIAM J. Math. Anal.
Year: 2016
We consider the minimization problem of an anisotropic energy in classes of $d$-rectifiable varifolds in $\mathbb R^n$, closed under Lipschitz deformations and encoding a suitable notion of boundary. We prove that any minimizing sequence with density uniformly bounded from below converges (up to subsequences) to a $d$-rectifiable varifold. Moreover, the limiting varifold is integral, provided the minimizing sequence is made of integral varifolds with uniformly locally bounded anisotropic first variation.