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arXiv · 2207.06217

Almost minimizers for a sublinear system with free boundary

Daniela De Silva·Seongmin Jeon·Henrik Shahgholian
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Abstract

We study vector-valued almost minimizers of the energy functional $$\int_D\left(|\nabla\mathbf{u}|^2+\frac2{1+q}\left(\lambda_+(x)|\mathbf{u}^+|^{q+1}+\lambda_-(x)|\mathbf{u}^-|^{q+1}\right)\right)dx,\quad0 0$, we take the epiperimetric inequality approach and prove the regularity for both almost minimizers and the set of "regular" free boundary points.

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Daniela De Silva, Seongmin Jeon, Henrik Shahgholian. 2022-07-13. Almost minimizers for a sublinear system with free boundary. https://arxiv.org/abs/2207.06217

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