Elliptic Boundary Value Problems on Corner Domains: Smoothness and Asymptotics of Solutions: 1341 (Lecture Notes in Mathematics, 1341) - Softcover

Dauge, Monique

Softcover

ISBN 10: 354050169X ISBN 13: 9783540501695

Publisher: Springer, 1988

Synopsis

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.

Edition details

• Publisher: Springer
• Publication date: 1988
• Language: English
• ISBN 10: 354050169X
• ISBN 13: 9783540501695
• Binding: Paperback
• Number of pages: 272