# Regularity of nonlinear generalized functions: a counterexample in the nonstandard setting

29 Mar 2016  ·  Vernaeve H. ·

Regularity theory in generalized function algebras of Colombeau type is largely based on the notion of ${\mathcal G}^\infty$-regularity, which reduces to $C^\infty$-regularity when restricted to Schwartz distributions. Surprisingly, in the nonstandard version of the Colombeau algebras, this basic property of ${\mathcal G}^\infty$-regularity does not hold...

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Functional Analysis Analysis of PDEs