Regular nonlinear generalized functions and applications

A. Delcroix

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Microlocal analysis in the dual of a Colombeau algebra: generalized wave front sets and noncharacteristic regularity.

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The New York Journal of Mathematics [electronic only]

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Comparison of Some Solution Concepts for Linear First-order Hyperbolic Differential Equations With Non-smooth Coefficients

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On the unique extension problem for functionals of the calculus of variations

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Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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By drawing inspiration from the treatment of the non parametric area problem, an abstract functional is considered, defined for every open set in a given class of open subsets of $R^{n}$ and every function in $C^{\infty} (R^{n})$ , and verifying suitable assumptions of measure theoretic type, of invariance, convexity, and lower semicontinuity. The problem is discussed of the possibility of extending it, and of the uniqueness of such extension, to a functional verifying analogous properties, but defined in wider...