19 citations · 69 across the 31 of their papers we have counts for
6 papers · 1 filter
Qualitative properties of free boundaries for the exterior Bernoulli problem for the half Laplacian
Sven Jarohs, Tadeusz Kulczycki, Paolo Salani
In this work, we study the asymptotic behavior of the free boundary of the solution to the exterior Bernoulli problem for the half Laplacian when the Bernoulli's gradient parameter…
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…
A parabolic PDE-based approach to Borell--Brascamp--Lieb inequality
Kazuhiro Ishige, Qing Liu, Paolo Salani
In this paper, we provide a new PDE proof for the celebrated Borell--Brascamp--Lieb inequality. Our approach reveals a deep connection between the Borell--Brascamp--Lieb inequality…
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…