Lower semicontinuity and relaxation of linear-growth integral functionals under PDE constraints
| Autor: | Filip Rindler, Adolfo Arroyo-Rabasa, Guido De Philippis |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
49J45 (primary)
49Q20 35E99 Applied Mathematics 010102 general mathematics Mathematical proof 01 natural sciences Measure (mathematics) Convexity 010101 applied mathematics functional on measures Mathematics - Analysis of PDEs Settore MAT/05 - Analisi Matematica FOS: Mathematics Order (group theory) Applied mathematics Gravitational singularity Relaxation (approximation) 0101 mathematics Linear growth QA Lower semicontinuity Analysis Geometry and topology Mathematics Analysis of PDEs (math.AP) |
| Zdroj: | Advances in Calculus of Variations |
| ISSN: | 1864-8266 |
| Popis: | 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. 43 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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