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Lower semicontinuity and relaxation of linear-growth integral functionals under PDE constraints
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Arroyo-Rabasa, Adolfo, de Philippis, Guido and Rindler, Filip (2020) Lower semicontinuity and relaxation of linear-growth integral functionals under PDE constraints. Advances in the Calculus of Variations, 13 (3). pp. 219-255. doi:10.1515/acv-2017-0003 ISSN 1864-8266.
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Official URL: https://doi.org/10.1515/acv-2017-0003
Abstract
We show general lower semicontinuity and relaxation theorems for linear-growth integral functionals defined on vector measures that satisfy linear PDE side constraints (of arbitrary order). These results generalize several known lower semicontinuity and relaxation theorems for BV, BD, and for more general first-order linear PDE side constrains. Our proofs are based on recent progress in the understanding of singularities of measure solutions to linear PDEs and of the generalized convexity notions corresponding to these PDE constraints.
Item Type: | Journal Article | ||||||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||
Library of Congress Subject Headings (LCSH): | Calculus of variations, Relaxation methods (Mathematics), Differential equations, Partial, Functionals, Functions of complex variables | ||||||||||||
Journal or Publication Title: | Advances in the Calculus of Variations | ||||||||||||
Publisher: | De Gruyter | ||||||||||||
ISSN: | 1864-8266 | ||||||||||||
Official Date: | 1 July 2020 | ||||||||||||
Dates: |
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Volume: | 13 | ||||||||||||
Number: | 3 | ||||||||||||
Page Range: | pp. 219-255 | ||||||||||||
DOI: | 10.1515/acv-2017-0003 | ||||||||||||
Status: | Peer Reviewed | ||||||||||||
Publication Status: | Published | ||||||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||||||
Date of first compliant deposit: | 29 January 2018 | ||||||||||||
Date of first compliant Open Access: | 11 January 2019 | ||||||||||||
RIOXX Funder/Project Grant: |
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