Almost minimizers for a singular system with free boundary

Daniela De Silva; Seongmin Jeon; Henrik Shahgholian

Almost minimizers for a singular system with free boundary

Analysis of PDEs 2021-12-02 v1

Authors: Daniela De Silva , Seongmin Jeon , Henrik Shahgholian

Abstract

In this paper we study vector-valued almost minimizers of the energy functional $\int_D\left(|\nabla\mathbf{u}|^2+2|\mathbf{u}|\right)\,dx .$ We establish the regularity for both minimizers and the "regular" part of the free boundary. The analysis of the free boundary is based on Weiss-type monotonicity formula and the epiperimetric inequality for the energy minimizers.

Keywords

minimizers energy minimization free boundary problem

Cite

@article{arxiv.2112.00676,
  title  = {Almost minimizers for a singular system with free boundary},
  author = {Daniela De Silva and Seongmin Jeon and Henrik Shahgholian},
  journal= {arXiv preprint arXiv:2112.00676},
  year   = {2021}
}

Comments

25 pages

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