Elliptic boundary value problems on corner domains : smoothness and asymptotics of solutions
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Bibliographic Information
Elliptic boundary value problems on corner domains : smoothness and asymptotics of solutions
（Lecture notes in mathematics, 1341）
Springer-Verlag, c1988
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Library & Science Information Center, Osaka Prefecture University
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
L/N||LNM||13418810045S
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
gwdc19:510/L4972070097406
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Note
Bibliography: p. [253]-257
Includes indexes
Description and Table of Contents
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.
Table of 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.
by "Nielsen BookData"