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On the structure of divergence-free measures on R^2
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Bonicatto, Paolo and Gusev, Nikolay A. (2021) On the structure of divergence-free measures on R^2. Advances in Calculus of Variations, 15 (4). pp. 879-911. doi:10.1515/acv-2020-0066 ISSN 1864-8258.
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Official URL: https://doi.org/10.1515/acv-2020-0066
Abstract
e consider the structure of divergence-free vector measures on the plane. We show that suchmeasures can be decomposed into measures induced by closed simple curves. More generally, we show that ifthe divergence of a planar vector-valued measure is a signed measure, then the vector-valued measure can bedecomposed into measures induced by simple curves (not necessarily closed). As an application we general-ize certain rigidity properties of divergence-free vector fields to vector-valued measures. Namely, we show thatif a locally finite vector-valued measure has zero divergence, vanishes in the lower half-space and the normalcomponent of the unit tangent vector of the measure is bounded from below (in the upper half-plane), thenthe measure is identically zero.
Item Type: | Journal Article | ||||||||||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||
Library of Congress Subject Headings (LCSH): | Vector-valued measures, Divergence theorem, Superposition principle (Physics) | ||||||||||||
Journal or Publication Title: | Advances in Calculus of Variations | ||||||||||||
Publisher: | Walter de Gruyter GmbH & Co. KG | ||||||||||||
ISSN: | 1864-8258 | ||||||||||||
Official Date: | 9 January 2021 | ||||||||||||
Dates: |
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Volume: | 15 | ||||||||||||
Number: | 4 | ||||||||||||
Page Range: | pp. 879-911 | ||||||||||||
DOI: | 10.1515/acv-2020-0066 | ||||||||||||
Status: | Peer Reviewed | ||||||||||||
Publication Status: | Published | ||||||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||||||
Date of first compliant deposit: | 26 November 2020 | ||||||||||||
Date of first compliant Open Access: | 9 January 2022 | ||||||||||||
RIOXX Funder/Project Grant: |
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