Hölder--Zygmund regularity in algebras of generalized functions

DOI10.4171/ZAA/1191zbMath1111.46023arXivmath/0112222MaRDI QIDQ1885059

Günther Hörmann

Publication date: 28 October 2004

Published in: Zeitschrift für Analysis und ihre Anwendungen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0112222

zbMATH Keywords

Hölder continuityZygmund classesalgebras of generalised functionsgeneralised solutions of differential equations

Mathematics Subject Classification ID

Related Items (17)

Notes on regularity results in Colombeau algebras ⋮ Optimal embeddings of ultradistributions into differential algebras ⋮ System of nonlinear Volterra's integral equations with polar kernel and singularities ⋮ Distributional solution concepts for the Euler–Bernoulli beam equation with discontinuous coefficients ⋮ Besov regularity in non-linear generalized functions ⋮ Regularity properties of distributions through sequences of functions ⋮ Classes of Generalized Functions with Finite Type Regularities ⋮ Harmonic generalized functions in generalized function algebras ⋮ \(L^p\) and Sobolev boundedness of pseudodifferential operators with non-regular symbol: a regularisation approach ⋮ Geometrical embeddings of distributions into algebras of generalized functions ⋮ Generalized Fourier Integral Operators on Spaces of Colombeau Type ⋮ Factorization of second-order strictly hyperbolic operators with logarithmic slow scale coefficients and generalized microlocal approximations ⋮ The wave equation on singular space-times ⋮ Real analytic generalized functions ⋮ Generalized solutions for the Euler-Bernoulli model with distributional forces ⋮ Wave-type equations of low regularity ⋮ Topological structures in Colombeau algebras: Topological \(\widetilde{\mathbb C}\)-modules and duality theory

Cites Work

• Hyperbolic systems with discontinuous coefficients: Generalized solutions and a transmission problem in acoustics
• Generalized solutions to symmetric hyperbolic systems with discontinuous coefficients: The multidimensional case
• Lectures on nonlinear hyperbolic differential equations
• Wavelets, Vibrations and Scalings
• Microlocal analysis and global solutions of some hyperbolic equations with discontinuous coefficients
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