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

ISBN-13: 9789048155453 / Angielski / Miękka / 2010 / 176 str.

V. Vasil'ev

Opis

This monograph is devoted to the development of a new approach to studying elliptic differential and integro-differential (pseudodifferential) equations and their boundary problems in non-smooth domains. This approach is based on a special representation of symbols of elliptic operators called wave factorization. In canonical domains, for example, the angle on a plane or a wedge in space, this yields a general solution, and then leads to the statement of a boundary problem. Wave factorization has also been used to obtain explicit formulas for solving some problems in diffraction and elasticity theory.

Audience: This volume will be of interest to mathematicians, engineers, and physicists whose work involves partial differential equations, integral equations, operator theory, elasticity and viscoelasticity, and electromagnetic theory. It can also be recommended as a text for graduate and postgraduate students for courses in singular integral and pseudodifferential equations.

Spis treści

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.