The De Giorgi measure and an obstacle problem related to minimal surfaces in metric spaces

DOI10.1016/j.matpur.2009.10.006zbMath1211.49055OpenAlexW2039433959WikidataQ109993981 ScholiaQ109993981MaRDI QIDQ981630

Juha Kinnunen, Heli Tuominen, Riikka Korte, Nageswari Shanmugalingam

Publication date: 1 July 2010

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matpur.2009.10.006

zbMATH Keywords

relaxed problemfunctions of bounded variationcapacitiesboxing inequality

Mathematics Subject Classification ID

Contents, measures, outer measures, capacities (28A12) Variational problems in a geometric measure-theoretic setting (49Q20) Functions of bounded variation, generalizations (26A45)

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Cites Work

• Adams inequality on metric measure spaces
• Functions of bounded variation on ``good metric spaces
• On the semicontinuity and the relaxation for integrals with respect to the Lebesgue measure added to integrals with respect to a Radon measure
• Lectures on analysis on metric spaces
• Fine properties of sets of finite perimeter in doubling metric measure spaces
• Relaxation of the non-parametric Plateau problem with an obstacle
• Newtonian spaces: An extension of Sobolev spaces to metric measure spaces
• Lebesgue points and capacities via boxing inequality in metric spaces
• Some fine properties of sets of finite perimeter in Ahlfors regular metric measure spaces
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