Indecomposable sets of finite perimeter in doubling metric measure spaces
| Autor: | Enrico Pasqualetto, Paolo Bonicatto, Tapio Rajala |
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| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Social connectedness variaatiolaskenta Space (mathematics) 01 natural sciences Measure (mathematics) differentiaaligeometria Perimeter Mathematics - Analysis of PDEs Mathematics - Metric Geometry 0103 physical sciences FOS: Mathematics 0101 mathematics Extreme point Representation (mathematics) Mathematics Applied Mathematics 010102 general mathematics differential equations Metric Geometry (math.MG) metriset avaruudet Functional Analysis (math.FA) Mathematics - Functional Analysis Metric (mathematics) mittateoria 010307 mathematical physics variation 26B30 53C23 Indecomposable module Analysis Analysis of PDEs (math.AP) |
| Zdroj: | Calculus of Variations and Partial Differential Equations |
| ISSN: | 1432-0835 0944-2669 |
| Popis: | We study a measure-theoretic notion of connectedness for sets of finite perimeter in the setting of doubling metric measure spaces supporting a weak $(1,1)$-Poincar\'{e} inequality. The two main results we obtain are a decomposition theorem into indecomposable sets and a characterisation of extreme points in the space of BV functions. In both cases, the proof we propose requires an additional assumption on the space, which is called isotropicity and concerns the Hausdorff-type representation of the perimeter measure. Comment: 32 pages |
| Databáze: | OpenAIRE |
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