Inhomogeneous global minimizers to the one-phase free boundary problem

Daniela De Silva, David Jerison, Henrik Shahgholian

Given a global 1-homogeneous minimizer $U_0$ to the Alt-Caffarelli energy functional, with $sing(F(U_0))=\{0\}$, we provide a foliation of the half-space $\R^{n} \times [0,+\inft…