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arXiv · 2601.21486

The Daugavet property for Sobolev spaces over the plane

Samir Hamad
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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.

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Samir Hamad. 2026-01-29. The Daugavet property for Sobolev spaces over the plane. https://arxiv.org/abs/2601.21486

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