Elliptic Boundary Value Problems in Domains with Point Singularities

✍ Scribed by Rossmann, Jürgen; Kozlov, Vladimir; Mazʹi︠a︡, V. G

• Publisher: American Mathematical Society
• Year: 1997
• Tongue: English
• Leaves: 426
• Series: Mathematical surveys and monographs no. 52
• Category: Library

✦ Synopsis

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

✦ Table of Contents

Content: Ch. 1. Boundary value problems for ordinary differential equations on the half-axis --
Ch. 2. Elliptic boundary value problems in the half-space --
Ch. 3. Elliptic boundary value problems in smooth domains --
Ch. 4. Variants and extensions --
Ch. 5. Elliptic boundary value problems in an infinite cylinder --
Ch. 6. Elliptic boundary value problems in domains with conical points --
Ch. 7. Elliptic boundary value problems in weighted Sobolev spaces with nonhomogeneous norms --
Ch. 8. Variants and extensions --
Ch. 9. Elliptic boundary value problems in domains with exterior cusps --
Ch. 10. Elliptic boundary value problems in domains with inside cusps.

✦ Subjects

Differential equations, Elliptic. Boundary value problems. Singularities (Mathematics) Équations différentielles elliptiques. Problèmes aux limites. Singularités (Mathématiques) Problème aux limites. Equations différentielles elliptiques. Boundary value problems Differential equations, Elliptic