Inhomogeneous global minimizers to the one-phase free boundary problem
Abstract
Given a global 1-homogeneous minimizer U0 to the Alt-Caffarelli energy functional, with sing(F(U0)) = \0\, we provide a foliation of the half-space n × [0,+∞) with dilations of graphs of global minimizers U ≤ U0 ≤ U with analytic free boundaries at distance 1 from the origin.
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