Calculus of Variations and Geometric Measure Theory
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E. Marconi

Rectifiability of entropy defect measures in a micromagnetics model

created by marconi on 25 Nov 2020

[BibTeX]

Preprint

Inserted: 25 nov 2020
Last Updated: 25 nov 2020

Year: 2020

Abstract:

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 $u$.


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