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arXiv · 2112.00676

Almost minimizers for a singular system with free boundary

Daniela De Silva·Seongmin Jeon·Henrik Shahgholian
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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.

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Daniela De Silva, Seongmin Jeon, Henrik Shahgholian. 2021-12-01. Almost minimizers for a singular system with free boundary. https://arxiv.org/abs/2112.00676

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