Calculus of Variations and Geometric Measure Theory

A. De Rosa - S. KolasiƄski

Equivalence of the ellipticity conditions for geometric variational problems

created by derosa on 18 Oct 2018
modified on 11 Jan 2022


Published Paper

Inserted: 18 oct 2018
Last Updated: 11 jan 2022

Journal: Comm. Pure App. Math.
Year: 2020

ArXiv: 1810.07262 PDF
Links: arxiv


We exploit the so called atomic condition, recently defined by De Philippis, De Rosa, and Ghiraldin in (Comm. Pure Appl. Math.) and proved to be necessary and sufficient for the validity of the anisotropic counterpart of the Allard rectifiability theorem. In particular, we address an open question of this seminal work, showing that the atomic condition implies the strict Almgren geometric ellipticity condition.