Seongmin Jeon: Almost minimizers for a cooperative system with free boundary

Abstract:

We consider vector-valued almost minimizers for the energy functional \(\int_{D}|\nabla u|^2+2/(1+q)|u|^{1+q}, 0\leq q< 1\). We discuss the regularity of almost minimizers and the "regular" part of the free boundary. The analysis of the free boundary is based on the application of the Weiss-type monotonicity formula and the epiperimetric inequality.

This is joint work with Daniela De Silva and Henrik Shahgholian.