Sobolev sheaves on the plane

M'hammed Oudrane

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arXiv · 2308.08077

Sobolev sheaves on the plane

M'hammed Oudrane

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Abstract

In this paper, 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. This paper serves as an introduction to a more general project on the sheafification of Sobolev spaces in higher dimensions.

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M'hammed Oudrane. 2023-08-16. Sobolev sheaves on the plane. https://arxiv.org/abs/2308.08077

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