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math.AP2019
Generic regularity of free boundaries for the obstacle problem
Alessio Figalli, Xavier Ros-Oton, Joaquim Serra
The goal of this paper is to establish generic regularity of free boundaries for the obstacle problem in . By classical results of Caffarelli, the free boundary is $C^…
math.AP2019
Stable solutions to semilinear elliptic equations are smooth up to dimension 9
Xavier Cabre, Alessio Figalli, Xavier Ros-Oton +1
In this paper we prove the following long-standing conjecture: stable solutions to semilinear elliptic equations are bounded (and thus smooth) in dimension . This result,…