Bessel capacities on compact manifolds and their relation to Poisson capacities
type: Item
instance of: scholarly article
title: Bessel capacities on compact manifolds and their relation to Poisson capacities
zbMATH Open document ID: 1118.31003
author: E. B. Dynkin
author: S. E. Kuznetsov
published in: Journal of Functional Analysis
publication date: 2007-01-16T00:00:00Z
review text: A motivation for this paper comes from the role the Choquet capacities play in the study of semilinear elliptic partial differential equations. In particular, recent progress in the classification of all positive solutions of the equation \(L u = u^ {\alpha }\) in a bounded smooth domain from \(\mathbb{R}^d\) was achieved by using, as a tool, capacities on the boundary of the manifold. The authors introduce two versions of Bessel capacities, on compact Lipschitz, respectively \(C^2\), \(N\)-dimensional manifold. They establish that these classes coincide when both are defined. Moreover, they prove that both versions of the Bessel capacities are equivalent to the so-called Poisson capacities associated with the Poisson kernel. If the manifold is the boundary of a bounded \(C^2\)-domain from \(\mathbb{R}^d\), then both versions of the Bessel capacities are equivalent to the Poisson capacities.
reviewed by: Liliana Popa
Mathematics Subject Classification ID: 31C15
Mathematics Subject Classification ID: 31C12
Mathematics Subject Classification ID: 60J45
zbMATH DE Number: 5116363
zbMATH Keywords: Choquet capacities
zbMATH Keywords: Bessel capacities
zbMATH Keywords: Poisson capacities
zbMATH Keywords: Lipschitz manifolds
zbMATH Keywords: diffusions on \(C^2\)-manifolds
MaRDI profile type: Publication
full work available at URL: j.jfa.2006.05.010
OpenAlex ID: W2087890930
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DOI: 10.1016/J.JFA.2006.05.010
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description: scientific article; zbMATH DE number 5116363