Wave Factorization of Elliptic Symbols: Theory and Applications

Introduction to the Theory of Boundary Value Problems in Non-Smooth Domains
Softcover Nachdruck of hardcover 1. Auflage 2000
ISBN: 978-90-481-5545-3
Verlag: Springer Netherlands

Buch, Englisch, 176 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 295 g

To summarize briefly, this book is devoted to an exposition of the foundations of pseudo differential equations theory in non-smooth domains. The elements of such a theory already exist in the literature and can be found in such papers and monographs as [90,95,96,109,115,131,132,134,135,136,146, 163,165,169,170,182,184,214-218]. In this book, we will employ a theory that is based on quite different principles than those used previously. However, precisely one of the standard principles is left without change, the "freezing of coefficients" principle. The first main difference in our exposition begins at the point when the "model problem" appears. Such a model problem for differential equations and differential boundary conditions was first studied in a fundamental paper of V. A. Kondrat'ev [134]. Here also the second main difference appears, in that we consider an already given boundary value problem. In some transformations this boundary value problem was reduced to a boundary value problem with a parameter. -\ in a domain with smooth boundary, followed by application of the earlier results of M. S. Agranovich and M. I. Vishik. In this context some operator-function R('-\) appears, and its poles prevent invertibility; iffor differential operators the function is a polynomial on A, then for pseudo differential operators this dependence on. -\ cannot be defined. Ongoing investigations of different model problems are being carried out with approximately this plan, both for differential and pseudodifferential boundary value problems.

Zielgruppe

Research

Autoren/Hrsg.

Vasil'Ev, V.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Naturwissenschaften Physik Mechanik Klassische Mechanik, Newtonsche Mechanik
• Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis

Inhaltsverzeichnis

1. Distributions and their Fourier transforms.- 2. Multidimensional complex analysis.- 3. Sobolev-Slobodetskii spaces.- 4. Pseudodifferential operators and equations in a half-space.- 5. Wave factorization.- 6. Diffraction on a quadrant.- 7. The problem of indentation of a wedge-shaped punch.- 8. Equations in an infinite plane angle.- 9. General boundary value problems.- 10. The Laplacian in a plane infinite angle.- 11. Problems with potentials.- Appendix 1: The multidimensional Riemann problem.- Appendix 2: Symbolic calculus, Noether property, index, regularization.- Appendix 3: The Mellin transform.- References.