Almost minimizers for a singular system with free boundary
Daniela De Silva, Seongmin Jeon, Henrik Shahgholian · Journal of Differential Equations · 2022
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.