Elliptic Boundary Value Problems on Corner Domains : Smoothness and Asymptotics of Solutions / by Monique Dauge.

Format:

Book

Author/Creator:

Dauge, Monique, 1956- author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1341.

Lecture Notes in Mathematics, 0075-8434 ; 1341

Language:

English

Subjects (All):

Global analysis (Mathematics).

Analysis.

Local Subjects:

Analysis.

Physical Description:

1 online resource (VIII, 264 pages).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1988.

System Details:

text file PDF

Summary:

This research monograph focusses on a large class of variational elliptic problems with mixed boundary conditions on domains with various corner singularities, edges, polyhedral vertices, cracks, slits. In a natural functional framework (ordinary Sobolev Hilbert spaces) Fredholm and semi-Fredholm properties of induced operators are completely characterized. By specially choosing the classes of operators and domains and the functional spaces used, precise and general results may be obtained on the smoothness and asymptotics of solutions. A new type of characteristic condition is introduced which involves the spectrum of associated operator pencils and some ideals of polynomials satisfying some boundary conditions on cones. The methods involve many perturbation arguments and a new use of Mellin transform. Basic knowledge about BVP on smooth domains in Sobolev spaces is the main prerequisite to the understanding of this book. Readers interested in the general theory of corner domains will find here a new basic theory (new approaches and results) as well as a synthesis of many already known results; those who need regularity conditions and descriptions of singularities for numerical analysis will find precise statements and also a means to obtain further one in many explicit situtations.

Contents:

Preliminaries

Fredholm and semi-Fredholm results

Proofs

Two-dimensional domains

Singularities along the edges

Laplace operator

Variational boundary value problems on smooth domains

Variational boundary value problems on polyhedral domains.

Other Format:

Printed edition:

ISBN:

9783540459422

Access Restriction:

Restricted for use by site license.