7 papers
Riemannian starshape and capacitary problems
Kazuhiro Ishige, Paolo Salani, Asuka Takatsu
We prove the Riemannian version of a classical Euclidean result: every level set of the capacitary potential of a starshaped ring is starshaped. In the Riemannian setting, we restr…
The Brunn-Minkowski inequality for the first eigenvalue of the Ornstein-Uhlenbeck operator and log-concavity of the relevant eigenfunction
Andrea Colesanti, Elisa Francini, Galyna Livshyts +1
We prove that the first (nontrivial) Dirichlet eigenvalue of the Ornstein-Uhlenbeck operator as a function of the domain, is convex with r…
Positive solutions of a critical equation in sub-Finsler geometry
Nicola Garofalo, Paolo Salani
We compute a two-parameter family of explicit positive solutions of a critical Yamabe type equation for a nonlinear operator that sits at the intersection of Finsler and sub-Rieman…
A fundamental solution for a subelliptic operator in Finsler geometry
Federica Dragoni, Nicola Garofalo, Gianmarco Giovannardi +1
We introduce a class of nonlinear partial differential equations in a product space which are at the interface of Finsler and sub-Riemannian geometry. To such equations we associat…
On the Bernoulli free boundary problems for the half Laplacian and for the spectral half Laplacian
Sven Jarohs, Tadeusz Kulczycki, Paolo Salani
We study the exterior and interior Bernoulli problems for the half Laplacian and the interior Bernoulli problem for the spectral half Laplacian. We concentrate on the existence and…
Optimal concavity of the torsion function
A. Henrot, C. Nitsch, P. Salani +1
In this short note we consider an unconventional overdetermined problem for the torsion function: let and be a bounded open set in whose torsion functi…