Geometric properties of solutions to elliptic PDE's in Gauss space and related Brunn-Minkowski type inequalities
Abstract
We prove a Brunn-Minkowski type inequality for the first (nontrivial) Dirichlet eigenvalue of the weighted p -operator − Δ p , γ u = − div ( | ∇ u | p − 2 ∇ u ) + ( x , ∇ u ) | ∇ u | p − 2 , where p > 1 , in the class of bounded Lipschitz domains in R n . We also prove that the corresponding positive eigenfunctions are log-concave if the domain is convex.
Fields of Study & Subjects
Point processes and geometric inequalities
Geometric Analysis and Curvature Flows
Nonlinear Partial Differential Equations
Publication details
- Journal / source
- Advances in Mathematics
- Publisher
- Elsevier BV
- Volume
- 489
- Pages
- 110827–110827
- Publication date
- 30 January 2026
- Language
- EN