Bulletin: Classe des sciences mathematiques et natturalles 2006 Volume 133, Issue 31, Pages: 147-162
https://doi.org/10.2298/BMAT0631148O
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Regularity theory in Colombeau algebras
Oberguggenberger M. (Institut f¨ur Grundlagen der Bauingenieurwissenschaften, Innsbruck, Austria)
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. AMS Mathematics Subject Classification (2000): 35D05, 35L60, 46F30.
Keywords: Colombeau algebras, partial differential equations, regularity of solutions