Indecomposable sets of finite perimeter in doubling metric measure spaces
Bonicatto, P., Pasqualetto, E., & Rajala, T. (2020). Indecomposable sets of finite perimeter in doubling metric measure spaces. Calculus of Variations and Partial Differential Equations, 59(2), Article 63. https://doi.org/10.1007/s00526-020-1725-7
DisciplineMatematiikkaAnalyysin ja dynamiikan tutkimuksen huippuyksikköMathematicsAnalysis and Dynamics Research (Centre of Excellence)
© 2020 the Authors
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)-Poincaré 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.
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Related funder(s)Academy of Finland
Funding program(s)Research costs of Academy Research Fellow, AoF; Research post as Academy Research Fellow, AoF; Academy Project, AoF; Centre of Excellence, AoF
Additional information about fundingOpen access funding provided by University of Jyväskylä (JYU). The first named author acknowledges ERC Starting Grant 676675 FLIRT. The second and third named authors are partially supported by the Academy of Finland, Projects 274372, 307333, 312488, and 314789.
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