Calculus of Variations and Geometric Measure Theory

A. De Rosa

Minimization of anisotropic energies in classes of rectifiable varifolds

created by derosa on 24 Nov 2016
modified on 11 Jan 2022


Published Paper

Inserted: 24 nov 2016
Last Updated: 11 jan 2022

Journal: SIAM J. Math. Anal.
Year: 2018
Links: ArXiv link


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.