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Lower semicontinuity and relaxation of linear-growth integral functionals under PDE constraints

Lower semicontinuity and relaxation of linear-growth integral functionals under PDE constraints AbstractWe 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Calculus of Variations de Gruyter

Lower semicontinuity and relaxation of linear-growth integral functionals under PDE constraints

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References (34)

Publisher
de Gruyter
Copyright
© 2021 Walter de Gruyter GmbH, Berlin/Boston
ISSN
1864-8266
eISSN
1864-8266
DOI
10.1515/acv-2017-0003
Publisher site
See Article on Publisher Site

Abstract

AbstractWe 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.

Journal

Advances in Calculus of Variationsde Gruyter

Published: Jul 1, 2020

Keywords: Lower semicontinuity; functional on measures; generalized Young measure; 49J45; 35J50; 28B05; 49Q20; 74B05

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