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Main Author: Oudrane, M'hammed
Format: Preprint
Published: 2023
Subjects:
Online Access:https://arxiv.org/abs/2308.08077
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author Oudrane, M'hammed
author_facet Oudrane, M'hammed
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2308_08077
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Sobolev sheaves on the plane
Oudrane, M'hammed
Metric Geometry
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.
title Sobolev sheaves on the plane
topic Metric Geometry
url https://arxiv.org/abs/2308.08077