Almost minimizers for a singular system with free boundary
Abstract
In this paper we study vector-valued almost minimizers of the energy functional ∫D(|∇u|2+2|u|)\,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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