The Daugavet property for Sobolev spaces over the plane
Abstract
We show that $W^{1,1}(\mathbb{R}^2)$ has the Daugavet property when endowed with the norm induced by the $L^1$-norm of the gradient, but fails to have the slice diameter two property when equipped with the usual Sobolev norm.
Fields of Study & Subjects
Advanced Banach Space Theory
Mathematical Inequalities and Applications
Advanced Operator Algebra Research
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 29 January 2026
- Document type
- Preprint