On the fully nonlinear Alt-Phillips equation (2008.06567v2)

Published 14 Aug 2020 in math.AP

Abstract: For a parameter $\gamma\in(1,2)$, we study the fully nonlinear version of the Alt-Phillips equation, $F(D^{2u)=u^{\gamma-1}$,} for $u\ge 0.$ We establish the optimal regularity of the solution, as well as the $C^1$ regularity of the regular part of the free boundary.

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