Dimensional estimates and rectifiability for measures satisfying linear PDE constraints
| Autor: | Adolfo Arroyo-Rabasa, Filip Rindler, Guido De Philippis, Jonas Hirsch |
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| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
General theorem 010102 general mathematics Scalar (mathematics) A-free measure Bounded deformation Mathematical proof 01 natural sciences Functional Analysis (math.FA) Mathematics - Functional Analysis 010101 applied mathematics Mathematics - Analysis of PDEs dimensional estimate Settore MAT/05 - Analisi Matematica Bounded function FOS: Mathematics PDE constraint Mathematics::Metric Geometry Rectifiability Geometry and Topology 0101 mathematics QA Analysis Analysis of PDEs (math.AP) Mathematics |
| Zdroj: | Geometric and Functional Analysis |
| ISSN: | 1420-8970 1016-443X |
| Popis: | We establish the rectifiability of measures satisfying a linear PDE constraint. The obtained rectifiability dimensions are optimal for many usual PDE operators, including all first-order systems and all second-order scalar operators. In particular, our general theorem provides a new proof of the rectifiability results for functions of bounded variations (BV) and functions of bounded deformation (BD). For divergence-free tensors we obtain refinements and new proofs of several known results on the rectifiability of varifolds and defect measures. Comment: 17 pages; to appear in GAFA |
| Databáze: | OpenAIRE |
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