Elliptic Boundary Value Problems on Corner Domains

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August 1988



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.


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.
EAN: 9783540501695
ISBN: 354050169X
Untertitel: Smoothness and Asymptotics of Solutions. 'Lecture Notes in Mathematics'. 1988. Auflage. Book. Sprache: Englisch.
Verlag: Springer
Erscheinungsdatum: August 1988
Seitenanzahl: 276 Seiten
Format: kartoniert
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