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

Adolfo Arroyo-Rabasa, Guido De Philippis, Filip Rindler

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)219-255
Number of pages37
JournalAdvances in Calculus of Variations
Volume13
Issue number3
DOIs
StatePublished - Jul 1 2020

Keywords

  • Functional on measures
  • Lower semicontinuity

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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