On the geometry and regularity of largest subsolutions for a free boundary problem in R2: elliptic case

摘要

We consider a one-phase exterior Bernoulli type free boundary problem inR2 with a non constant, only continuous, free boundary condition. In this article, we present geometry and regularity properties of the largest viscosity subsolution of this problem. Moreover, we provide density bounds for the positivity set and its complement near the free boundary.