Boundary measures, generalized Gauss-Green formulas, and mean value property in metric measure spaces

DOI10.4171/RMI/843zbMath1333.30071arXiv1304.4352WikidataQ109994385 ScholiaQ109994385MaRDI QIDQ748333

Niko Marola, Nageswari Shanmugalingam, Michele~jun. Miranda

Publication date: 20 October 2015

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1304.4352

zbMATH Keywords

Poincaré inequalityharmonic functionsdoubling measuremetric measure space

Mathematics Subject Classification ID

Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Analysis on metric spaces (30L99)

Related Items (9)

On BV functions and essentially bounded divergence-measure fields in metric spaces ⋮ An analog of the Neumann problem for the 1-Laplace equation in the metric setting: existence, boundary regularity, and stability ⋮ Characterizations of sets of finite perimeter using heat kernels in metric spaces ⋮ On locally essentially bounded divergence measure fields and sets of locally finite perimeter ⋮ Extensions and traces of BV functions in rough domains and generalized Cheeger sets ⋮ Trace theorems for functions of bounded variation in metric spaces ⋮ Neumann problem for \(p\)-Laplace equation in metric spaces using a variational approach: existence, boundedness, and boundary regularity ⋮ The Gauss-Green theorem in stratified groups ⋮ Rough traces of BV functions in metric measure spaces

Cites Work

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• Comparison of BV norms in weighted Euclidean spaces
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• Local behavior of \(p\)-harmonic Green's functions in metric spaces
• Differentiability of Lipschitz functions on metric measure spaces
• Dirichlet forms and symmetric Markov processes
• Singular functions on metric measure spaces.
• Modulus and the Poincaré inequality on metric measure spaces
• Fat sets and pointwise boundary estimates for \(p\)-harmonic functions in metric spaces
• Fine properties of sets of finite perimeter in doubling metric measure spaces
• Definitions of Sobolev classes on metric spaces
• Measure-theoretic analysis and nonlinear conservation laws
• The Dirichlet problem for p-harmonic functions on metric spaces
• Regularity of quasi-minimizers on metric spaces

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