The free boundary for a superlinear system

Abstract

In this paper, we study superlinear systems that give rise to free boundaries. Such systems appear for example from the minimization of the energy functional(Formula presented) but solutions can be also understood in an ad hoc viscosity way.First, we prove the optimal regularity of minimizers using a variational approach. Then, we apply a linearization technique to establish the C1,α[jls-end-space/]-regularity of the “flat” part of the free boundary via a viscosity method. Finally, for minimizing free boundaries, we extend this result to analyticity.