Sobolev sheaves on the plane
Volume 137 / 2026
Annales Polonici Mathematici 137 (2026), 155-195
MSC: Primary 46E35; Secondary 32B20
DOI: 10.4064/ap250408-1-12
Published online: 3 November 2026
Abstract
We show that for any integer $k \in \mathbb {N}$ there exists a Sobolev sheaf (in the sense of Lebeau) on any definable site of $\mathbb {R}^2$ that agrees with Sobolev spaces on cuspidal domains. We also provide a complete computation of the cohomology of these sheaves using the notion of good direction introduced by Valette.
