Notes on regularity results in Colombeau algebras

DOI10.1080/10652460500436601zbMath1091.35019OpenAlexW1993507750MaRDI QIDQ5291795

Michael Oberguggenberger

Publication date: 22 May 2006

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10652460500436601

zbMATH Keywords

regularity of solutions

Mathematics Subject Classification ID

First-order nonlinear hyperbolic equations (35L60) Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) (46F30)

Related Items (2)

Propagation of singularities for generalized solutions to nonlinear wave equations ⋮ Wave-type equations of low regularity

Cites Work

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• Integration and microlocal analysis in Colombeau algebras of generalized functions
• First-order hyperbolic pseudodifferential equations with generalized symbols
• Hölder--Zygmund regularity in algebras of generalized functions
• Generalized integral operators and Schwartz kernel type theorems
• Topological structures in Colombeau algebras: Investigation of the duals of \(\mathcal G_c(\Omega)\), \(\mathcal G(\Omega)\) and \(\mathcal G_{\mathcal S}(\mathbb R^n)\)
• MICROLOCAL ANALYSIS OF GENERALIZED FUNCTIONS: PSEUDODIFFERENTIAL TECHNIQUES AND PROPAGATION OF SINGULARITIES
• Microlocal properties of basic operations in Colombeau algebras
• Microlocal analysis and global solutions of some hyperbolic equations with discontinuous coefficients

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