EMIS ELibM Electronic Journals Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques naturelles / sciences mathematiques
Vol. CXXXIII, No. 31, pp. 147–162 (2006)

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Regularity theory in Colombeau algebras

M. Oberguggenberger

Institut für Grundlagen der Bauingenieurwissenschaften, Universität Innsbruck, A-6020 Innsbruck, Austria, E-mail: Michael.Oberguggenberger@uibk.ac.at

Abstract: This paper introduces and discusses various notions of regularity of solutions to partial differential equations in Colombeau algebras. The aim is to suggest a number of approaches that allow to extend the regularity theory to nonlinear equations. A relation with the notion of delta waves is observed.

Keywords: Colombeau algebras, partial differential equations, regularity of solutions

Classification (MSC2000): 35D05, 35L60, 46F30

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Electronic fulltext finalized on: 10 Jun 2006. This page was last modified: 20 Jun 2011.

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