Topology on asymptotic algebras of generalized functions and applications
type: Item
instance of: scholarly article
title: Topology on asymptotic algebras of generalized functions and applications
zbMATH Open document ID: 0952.46029
author: Antoine Delcroix
author: D. Scarpalezos
published in: Monatshefte für Mathematik
publication date: 2001-01-15T00:00:00Z
review text: Nonlinear problems with singular coefficients or with singular additional conditions require the algebras of generalized functions. The authors of this paper construct such algebras of Colombeau type (called asymptotic algebras) starting from a locally convex metrizable topological space and using an asymptotic scale. A Hausdorff topology (called sharp topology) is defined in such an algebra. They also introduce temperate nonlinear mappings between them. Topological properties and the continuity of operations in such algebras have been analyzed. At the end, the authors treat a semilinear elliptic Dirichlet problem as an application of these algebras.
Mathematics Subject Classification ID: 46F30
Mathematics Subject Classification ID: 35D99
Mathematics Subject Classification ID: 26E99
Mathematics Subject Classification ID: 34E10
zbMATH DE Number: 1417251
zbMATH Keywords: Colombeau extension
zbMATH Keywords: nonlinear problems with singular coefficients
zbMATH Keywords: algebras of generalized functions
zbMATH Keywords: algebras of Colombeau type
zbMATH Keywords: asymptotic algebras
zbMATH Keywords: sharp topology
zbMATH Keywords: temperate nonlinear mappings
zbMATH Keywords: semilinear elliptic Dirichlet problem
reviewed by: B. Stanković
MaRDI profile type: Publication
full work available at URL: s006050050001
OpenAlex ID: W2051205926
DOI: 10.1007/S006050050001
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description: scientific article; zbMATH DE number 1417251