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 $p$-operator \[ -Δ_{p,γ}u=-\text{div}(|\nabla u|^{p-2} \nabla u)+(x,\na…