
Elliptic Boundary Value Problems on Corner Domains
Smoothness and Asymptotics of Solutions
Monique Dauge(Author)
Springer (Publisher)
Published on 24. August 1988
Book
Paperback/Softback
VIII, 264 pages
978-3-540-50169-5 (ISBN)
Description
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.
More details
Series
Edition
1988 ed.
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
VIII, 264 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 16 mm
Weight
423 gr
ISBN-13
978-3-540-50169-5 (9783540501695)
DOI
10.1007/BFb0086682
Schweitzer Classification
Content
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.