Colombeau algebras on a \(C^{\infty{}}\)-manifold

DOI10.1016/0019-3577(91)90022-YzbMath0761.46022MaRDI QIDQ1190349

M. Damsma, J. W. de Roever

Publication date: 27 September 1992

Published in: Indagationes Mathematicae. New Series (Search for Journal in Brave)

zbMATH Keywords

Colombeau algebras\(C^ \infty\)-manifolddistribution in the sense of Colombeauinjective sheaf morphismquotient sheaf

Mathematics Subject Classification ID

Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.) (46M20) Distributions, generalized functions, distribution spaces (46F99) Topological linear spaces of test functions, distributions and ultradistributions (46F05)

Related Items (14)

Microlocal analysis of Colombeau's generalized functions on a manifold ⋮ Nonsmooth differential geometry and algebras of generalized functions ⋮ Sheaves of nonlinear generalized functions and manifold-valued distributions ⋮ Optimal regularization processes on complete Riemannian manifolds ⋮ Nonlinear tensor distributions on Riemannian manifolds ⋮ Geodesics in nonexpanding impulsive gravitational waves with Λ. II ⋮ Isomorphisms of algebras of generalized functions ⋮ Rapidly converging approximations and regularity theory ⋮ Suppleness of the sheaf of algebras of generalized functions on manifolds ⋮ Nonlinearity and self-interaction in physical field theories with singularities ⋮ Geometrical embeddings of distributions into algebras of generalized functions ⋮ Microlocal analysis of Colombeau's generalized functions: Propagation of singularities ⋮ A global theory of algebras of generalized functions ⋮ Generalized pseudo-Riemannian geometry

Cites Work

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• Hyperbolic systems with discontinuous coefficients: Generalized solutions and a transmission problem in acoustics
• A nonlinear theory of generalized functions.
• Multiplications of distributions in elasticity and hydrodynamics

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