Calculus of Variations and Geometric Measure Theory

E. Marconi

Rectifiability of entropy defect measures in a micromagnetics model

created by marconi on 25 Nov 2020
modified on 24 May 2021


Accepted Paper

Inserted: 25 nov 2020
Last Updated: 24 may 2021

Journal: Advances in Calc. Var.
Year: 2020


We study the fine properties of a class of weak solutions $u$ of the eikonal equation arising as asymptotic domain of a family of energy functionals introduced in (Rivière T, Serfaty S. Limiting domain wall energy for a problem related to micromagnetics. Comm Pure Appl Math 2001; 54(3):294-338). In particular we prove that the entropy defect measure associated to $u$ is concentrated on a 1-rectifiable set, which detects the jump-type discontinuities of $u$.