Covariant Poisson equation with compact Lie algebras

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dc.creatorSalmela, Antti
dc.date2002-11-13
dc.date.accessioned2026-07-07T04:29:34Z
dc.date.available2026-07-07T04:29:34Z
dc.descriptionThe covariant Poisson equation for Lie algebra-valued mappings defined in 3-dimensional Euclidean space is studied using functional analytic methods. Weighted covariant Sobolev spaces are defined and used to derive sufficient conditions for the existence and smoothness of solutions to the covariant Poisson equation. These conditions require, apart from suitable continuity, appropriate local integrability of the gauge potentials and global weighted integrability of the curvature form and the source. The possibility of nontrivial asymptotic behaviour of a solution is also considered. As a by-product, weighted covariant generalisations of Sobolev embeddings are established.
dc.description31 pages, LaTeX2e
dc.identifierhttps://arxiv.org/abs/math-ph/0211024
dc.identifierhttp://arxiv.org/abs/math-ph/0211024
dc.identifierJ.Math.Phys. 45 (2004) 2844-2863
dc.identifierdoi:10.1063/1.1763001
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57204
dc.subjectMathematical Physics
dc.subjectAnalysis of PDEs
dc.subject35J05, 35B65, 46E35
dc.titleCovariant Poisson equation with compact Lie algebras
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