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.;
2020-01-01
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.| File | Dimensione | Formato | |
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