Wave Factorization of Elliptic Symbols: Theory and Applications. Introduction to the Theory of Boundary Value Problems in Non-Smooth Domains.

Vasil'ev, Vladimir B.

ISBN 10: 0792365313 / ISBN 13: 9780792365310

Editore: Dordrecht, Kluwer., 2000

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IX, 176 p. Hardcover. Versand aus Deutschland / We dispatch from Germany via Air Mail. Einband bestoßen, daher Mängelexemplar gestempelt, sonst sehr guter Zustand. Imperfect copy due to slightly bumped cover, apart from this in very good condition. Stamped. Sprache: Englisch.

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Dati bibliografici

• Titolo: Wave Factorization of Elliptic Symbols: Theory and Applications. Introduction to the Theory of Boundary Value Problems in Non-Smooth Domains.
• Editore: Dordrecht, Kluwer.
• Data di pubblicazione: 2000
• Lingua: Inglese
• ISBN 10: 0792365313
• ISBN 13: 9780792365310
• Rilegatura: Rilegato
• Cataloghi dei venditori:
  • Mathematik

Descrizione articolo

Riassunto

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.

Contenuti

Preface. 1. Distributions and their Fourier transforms. 2. Multidimensional complex analysis. 3. Sobolev-Slobodetskii spaces. 4. Pseudodifferential operators and equations in 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. Index.