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  1. ; (, Bulletin of the London Mathematical Society)
    Abstract We develop the free boundary regularity for nonnegative minimizers of the Alt–Phillips functional for negative power potentialsand establish a ‐convergence result of the rescaled energies to the perimeter functional as . 
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  2. ; (, Journal für die reine und angewandte Mathematik (Crelles Journal))
    Abstract We study the regularity of free boundaries in the multiple elastic membrane problem in the plane. We prove the uniqueness of blow-ups, and that the free boundaries are C 1 , log {C^{1,\log}}-curves near a regular intersection point. 
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  3. ; (, Advances in Mathematics)
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  4. ; ; (, Calculus of Variations and Partial Differential Equations)
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  5. ; (, Advanced Nonlinear Studies)
    Abstract We investigate the rigidity of global minimizers u ≥ 0 u\ge 0 of the Alt-Phillips functional involving negative power potentials ∫ Ω ( ∣ ∇ u ∣ 2 + u − γ χ { u > 0 } ) d x , γ ∈ ( 0 , 2 ) , \mathop{\int }\limits_{\Omega }(| \nabla u{| }^{2}+{u}^{-\gamma }{\chi }_{\left\{u\gt 0\right\}}){\rm{d}}x,\hspace{1.0em}\gamma \in \left(0,2), when the exponent γ \gamma is close to the extremes of the admissible values. In particular, we show that global minimizers in R n {{\mathbb{R}}}^{n} are one-dimensional if γ \gamma is close to 2 and n ≤ 7 n\le 7 , or if γ \gamma is close to 0 and n ≤ 4 n\le 4 . 
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  6. ; (, Archive for Rational Mechanics and Analysis)
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