6 papers · 1 filter
Critical -Laplace equations with monotone coefficients: Liouville classification and a Schoen-type Harnack inequality
Yi Ru-Ya Zhang
We investigate positive weak solutions of the critical -Laplace equation where is a positive, bounded, continuous, and nonin…
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…
A Pohozaev-type neck proof of a conditional Harnack inequality in the critical -Laplacian setting
Guolin Qin, Yi Ru-Ya Zhang
We prove a conditional Schoen-type Harnack inequality for positive weak solutions of the critical -Laplace equation under a global critical Sobo…
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…
Serrin's overdetermined problem in rough domains
Alessio Figalli, Yi Ru-Ya Zhang
The classical Serrin's overdetermined theorem states that a bounded domain, which admits a function with constant Laplacian that satisfies both constant Dirichlet and Neumann…