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

Adolfo Arroyo-Rabasa; Filip Rindler; Guido De Philippis

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

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arxiv 1701.02230 v2 pith:2OF6R6UO submitted 2017-01-09 math.AP

Adolfo Arroyo-Rabasa , Guido De Philippis , Filip Rindler This is my paper

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keywords constraintslinearlowerrelaxationsemicontinuityfunctionalsgeneralintegral

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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.

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