New weighted inequalities on two–manifolds
Abstract
We establish a new class of weighted L^{2} Poincaré and elliptic functional inequalities on smooth two-manifolds with explicit constants, for a family of weights satisfying a differential equation. This family includes, in particular, weights comparable to products of positive powers of the geodesic distance to finitely many points. Our primary motivation is the derivation of estimates associated with a weighted Hodge decomposition for one-forms.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Advanced Harmonic Analysis Research
Geometric Analysis and Curvature Flows
Publication details
- Journal / source
- Rendiconti del Seminario Matematico della Università di Padova
- Publication date
- 29 July 2026
- Language
- EN