Wave Factorization of Elliptic Symbols: Theory and Applications (eBook)

Introduction to the Theory of Boundary Value Problems in Non-Smooth Domains

V. Vasil'ev (Autor)

eBook Download: PDF

2013
Springer Netherlands (Verlag)
978-94-015-9448-6 (ISBN)

Infos

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 "e;freezing of coefficients"e; principle. The first main difference in our exposition begins at the point when the "e;model problem"e; 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.

Produkt-Details

• Erscheint lt. Verlag: 9.3.2013
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Mechanik
• ISBN-10: 94-015-9448-1 / 9401594481
• ISBN-13: 978-94-015-9448-6 / 9789401594486