6533b7dbfe1ef96bd1271651
RESEARCH PRODUCT
Indecomposable sets of finite perimeter in doubling metric measure spaces
Enrico PasqualettoPaolo BonicattoTapio Rajalasubject
Pure mathematicsSocial connectednessvariaatiolaskentaSpace (mathematics)01 natural sciencesMeasure (mathematics)differentiaaligeometriaPerimeterMathematics - Analysis of PDEsMathematics - Metric Geometry0103 physical sciencesFOS: Mathematics0101 mathematicsExtreme pointRepresentation (mathematics)MathematicsApplied Mathematics010102 general mathematicsdifferential equationsMetric Geometry (math.MG)metriset avaruudetFunctional Analysis (math.FA)Mathematics - Functional AnalysisMetric (mathematics)mittateoria010307 mathematical physicsvariation26B30 53C23Indecomposable moduleAnalysisAnalysis of PDEs (math.AP)description
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2020-01-01 | Calculus of Variations and Partial Differential Equations |