Elliptic Boundary Value Problems in Domains with Point Singularities
Seiten
1997
American Mathematical Society (Verlag)
9780821807545 (ISBN)
American Mathematical Society (Verlag)
9780821807545 (ISBN)
Aims to treat a theory of elliptic boundary value problems in domains without singularities and in domains with conical or cuspidal points. This work focuses on fundamental results of the theory: estimates for solutions in different function spaces, regularity assertions and asymptotic formulas for the solutions near singular points.
This monograph systematically treats a theory of elliptic boundary value problems in domains without singularities and in domains with conical or cuspidal points. This exposition is self-contained and a priori requires only basic knowledge of functional analysis. Restricting to boundary value problems formed by differential operators and avoiding the use of pseudo-differential operators makes the book accessible for a wider readership. The authors concentrate on fundamental results of the theory: estimates for solutions in different function spaces, the Fredholm property of the operator of the boundary value problem, regularity assertions and asymptotic formulas for the solutions near singular points. A special feature of the book is that the solutions of the boundary value problems are considered in Sobolev spaces of both positive and negative orders. Results of the general theory are illustrated by concrete examples. The book may be used for courses in partial differential equations.
This monograph systematically treats a theory of elliptic boundary value problems in domains without singularities and in domains with conical or cuspidal points. This exposition is self-contained and a priori requires only basic knowledge of functional analysis. Restricting to boundary value problems formed by differential operators and avoiding the use of pseudo-differential operators makes the book accessible for a wider readership. The authors concentrate on fundamental results of the theory: estimates for solutions in different function spaces, the Fredholm property of the operator of the boundary value problem, regularity assertions and asymptotic formulas for the solutions near singular points. A special feature of the book is that the solutions of the boundary value problems are considered in Sobolev spaces of both positive and negative orders. Results of the general theory are illustrated by concrete examples. The book may be used for courses in partial differential equations.
Introduction Part 1: Boundary value problems for ordinary differential equations on the half-axis Elliptic boundary value problems in the half-space Elliptic boundary value problems in smooth domains Variants and extensions Part 2: Elliptic boundary value problems in an infinite cylinder Elliptic boundary value problems in domains with conical points Elliptic boundary value problems in weighted Sobolev spaces with nonhomogeneous norms Variants and extensions Part 3 Elliptic boundary value problems in domains with exterior cusps Elliptic boundary value problems in domains with inside cusps Bibliography Index List of symbols.
| Erscheint lt. Verlag | 30.9.1997 |
|---|---|
| Reihe/Serie | Mathematical Surveys and Monographs |
| Verlagsort | Providence |
| Sprache | englisch |
| Gewicht | 921 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| ISBN-13 | 9780821807545 / 9780821807545 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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