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.

Lower semicontinuity and relaxation of linear-growth integral functionals under PDE constraints / Arroyo-Rabasa, A.; De Philippis, G.; Rindler, F.. - In: ADVANCES IN CALCULUS OF VARIATIONS. - ISSN 1864-8266. - 13:3(2020), pp. 219-255. [10.1515/acv-2017-0003]

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

De Philippis,G.;
2020

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.
13
3
219
255
https://doi.org/10.1515/acv-2017-0003
https://arxiv.org/abs/1701.02230
https://www.degruyter.com/view/journals/acv/13/3/article-p219.xml
Arroyo-Rabasa, A.; De Philippis, G.; Rindler, F.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/85688
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