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The general class of Wasserstein Sobolev spaces: density of cylinder functions, reflexivity, uniform convexity and Clarkson's inequalities.
- Source :
-
Calculus of Variations & Partial Differential Equations . Sep2023, Vol. 62 Issue 7, p1-41. 41p. - Publication Year :
- 2023
-
Abstract
- We show that the algebra of cylinder functions in the Wasserstein Sobolev space H 1 , q (P p (X , d) , W p , d , m) generated by a finite and positive Borel measure m on the (p , d) -Wasserstein space (P p (X , d) , W p , d) on a complete and separable metric space (X , d) is dense in energy. As an application, we prove that, in case the underlying metric space is a separable Banach space B , then the Wasserstein Sobolev space is reflexive (resp. uniformly convex) if B is reflexive (resp. if the dual of B is uniformly convex). Finally, we also provide sufficient conditions for the validity of Clarkson's type inequalities in the Wasserstein Sobolev space. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09442669
- Volume :
- 62
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- Calculus of Variations & Partial Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 170040805
- Full Text :
- https://doi.org/10.1007/s00526-023-02543-1