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




E-Book Name Title for Download :Elliptic Boundary Value Problems on Corner Domains: Smoothness and Asymptotics of Solutions (Lecture Notes in Mathematics) (Format : pdf)

Plot : 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 semiFredholm 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.



Author(s) Book :Monique Dauge
E-Book Categories :
Publish Year :1988 Publisher : Springer
You can check by ISBN10: 038750169X; ISBN13: 9780387501697
Pages :259

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