Uniform estimates of Green functions and Sobolev-type inequalities on real and complex manifolds
Abstract
In this paper, we prove certain [Formula: see text] Sobolev-type and Poincaré-type inequalities for functions on real and complex manifolds for the gradient operator [Formula: see text], the Laplace operator [Formula: see text] and the operator [Formula: see text]. Integral representations for functions are key to get such inequalities. The proofs of the main results involve certain uniform estimates for the Green functions and their gradients on Riemannian manifolds, which are also established in this work.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Advanced Mathematical Modeling in Engineering
Publication details
- Journal / source
- International Journal of Mathematics
- Publisher
- World Scientific Pub Co Pte Ltd
- Publication date
- 4 September 2026
- Language
- EN