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.
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Michael Oberguggenberger (2006) studied this question.
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