10 papers
An anisotropic Serrin's problem in general domains
Alessio Figalli, Yi Ru-Ya Zhang
Serrin's symmetry theorem shows that the classical overdetermined torsion problem forces the domain to be a ball. Extending this rigidity statement to merely Lipschitz (and more ge…
Stable Semilinear Elliptic Equations: -Regularity à la Brezis and Dimensional Bounds for the Singular Set
Alessio Figalli, Federico Franceschini
We develop a quantitative partial regularity theory for stable solutions of \[ -Îu=f(u), \] where is increasing and convex. The theory is uniform in…
Sharp stability of Alexandrov's theorem for domains in the small-excess regime
Alessio Figalli, Yi Ru-Ya Zhang
We prove a sharp quantitative stability result for Alexandrov's theorem in arbitrary dimension for bounded open sets in a small-excess regime. More precisely, if $E\subset \m…
A dimension-free interpolation of Caffarelli's contraction theorem
Bader Ammari, Alessio Figalli
We prove global Lipschitz estimates for Brenier maps between probability measures on whose densities belong to the family $$ Ï_{U,\,p}=Z_{U,\, p}^{-1}\exp(-Î_p(U))…
Global regularity and free boundary geometry in the planar Choné-Rochet model
Shibing Chen, Alessio Figalli, Yi Ru-Ya Zhang
In this paper, we study minimizers of the Choné--Rochet variational problem in dimension two. We first establish global regularity on arbitrary bounded convex domains, and t…
Uniform boundedness for finite Morse index solutions to supercritical semilinear elliptic equations
Alessio Figalli, Yi Ru-Ya Zhang
We consider finite Morse index solutions to semilinear elliptic questions, and we investigate their smoothness. It is well-known that: - For , there exist Morse index solu…