Free boundaries of minimizers of the Alt-Phillips functional with negative powers γ ∈ (0,2) are C^∞ at regular points.
Savin,Regularity of flat level sets in phase transitions, Annals of Mathematics, 169 (2009), 41-78
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$C^{\infty}$ regularity of the Alt-Phillips Functional for negative powers
Free boundaries of minimizers of the Alt-Phillips functional with negative powers γ ∈ (0,2) are C^∞ at regular points.