6 papers
A Brunn--Minkowski inequality for the Hessian eigenvalue in convex domain
Jiahuan Li, Xi-Nan Ma, Paolo Salani
We use the deformation methods to obtain the strictly log concavity of solution of a class Hessian equation in bounded convex domain in , as an application we get t…
Preservation of F-convexity under the heat flow
Kazuhiro Ishige, Troy Petitt, Paolo Salani
We introduce the notion of F-convexity as a general extension of power convexity. We characterize the F-convexities preserved under the heat flow in the n-dimensional Euclidean spa…
A constant rank theorem for linear elliptic equations on the sphere with applications to the mixed Christoffel problem
A. Colesanti, M. Focardi, P. Guan +1
We study the mixed Christoffel problem for convex bodies providing sufficient conditions for its solution. Key to our approach is a constant rank theorem, following the a…
Log-concavity of solutions of parabolic equations related to the Ornstein-Uhlenbeck operator and applications
Andrea Colesanti, Lei Qin, Paolo Salani
In this paper, we investigate the log-concavity of the kernel for the parabolic Ornstein-Uhlenbeck operator in a bounded, convex domain. Consequently, we get the preservation of th…
Geometric properties of solutions to elliptic PDE's in Gauss space and related Brunn-Minkowski type inequalities
Andrea Colesanti, Lei Qin, Paolo Salani
We prove a Brunn-Minkowski type inequality for the first (nontrivial) Dirichlet eigenvalue of the weighted -operator \[ -Î_{p,γ}u=-\text{div}(|\nabla u|^{p-2} \nabla u)+(x,\na…
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…