Elliptic boundary value problems on corner domains : smoothness and asymptotics of solutions /
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 pr...
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| Format: | eBook |
| Language: | English |
| Published: |
Berlin ; New York :
Springer-Verlag,
[1988]
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| Series: | Lecture notes in mathematics (Springer-Verlag) ;
1341. |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
| 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. |
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| Item Description: | Electronic resource. |
| Physical Description: | 1 online resource (viii, 257 pages) : illustrations. |
| Format: | Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. |
| Bibliography: | Includes bibliographical references (pages [253]-257) and index. |
| ISBN: | 9783540459422 (electronic bk.) 3540459421 (electronic bk.) |
| ISSN: | 0075-8434 ; |