Elliptic Boundary Value Problems on Corner Domains

Elliptic Boundary Value Problems on Corner Domains
Title Elliptic Boundary Value Problems on Corner Domains PDF eBook
Author Monique Dauge
Publisher Springer
Pages 266
Release 2006-11-14
Genre Mathematics
ISBN 3540459421

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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.

Elliptic Boundary Value Problems on Corner Domains

Elliptic Boundary Value Problems on Corner Domains
Title Elliptic Boundary Value Problems on Corner Domains PDF eBook
Author Monique Dauge
Publisher
Pages 276
Release 2014-09-01
Genre
ISBN 9783662165232

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Elliptic Problems in Nonsmooth Domains

Elliptic Problems in Nonsmooth Domains
Title Elliptic Problems in Nonsmooth Domains PDF eBook
Author Pierre Grisvard
Publisher SIAM
Pages 426
Release 2011-10-20
Genre Mathematics
ISBN 1611972027

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Originally published: Boston: Pitman Advanced Pub. Program, 1985.

Elliptic Problems in Domains with Piecewise Smooth Boundaries

Elliptic Problems in Domains with Piecewise Smooth Boundaries
Title Elliptic Problems in Domains with Piecewise Smooth Boundaries PDF eBook
Author Sergey Nazarov
Publisher Walter de Gruyter
Pages 537
Release 2011-06-01
Genre Mathematics
ISBN 3110848910

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The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany

Boundary Value Problems and Integral Equations in Nonsmooth Domains

Boundary Value Problems and Integral Equations in Nonsmooth Domains
Title Boundary Value Problems and Integral Equations in Nonsmooth Domains PDF eBook
Author Martin Costabel
Publisher CRC Press
Pages 320
Release 1994-10-25
Genre Mathematics
ISBN 9780824793203

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Based on the International Conference on Boundary Value Problems and lntegral Equations In Nonsmooth Domains held recently in Luminy, France, this work contains strongly interrelated, refereed papers that detail the latest findings in the fields of nonsmooth domains and corner singularities. Two-dimensional polygonal or Lipschitz domains, three-dimensional polyhedral corners and edges, and conical points in any dimension are examined.

Elliptic Boundary Value Problems in Domains with Point Singularities

Elliptic Boundary Value Problems in Domains with Point Singularities
Title Elliptic Boundary Value Problems in Domains with Point Singularities PDF eBook
Author Vladimir Kozlov
Publisher American Mathematical Soc.
Pages 426
Release 1997
Genre Mathematics
ISBN 0821807544

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For graduate students and research mathematicians interested in partial differential equations and who have a basic knowledge of functional analysis. Restricted to boundary value problems formed by differential operators, avoiding the use of pseudo- differential operators. Concentrates on fundamental results such as estimates for solutions in different function spaces, the Fredholm property of the problem's operator, regularity assertions, and asymptotic formulas for the solutions of near singular points. Considers the solutions in Sobolev spaces of both positive and negative orders. Annotation copyrighted by Book News, Inc., Portland, OR

Wave Factorization of Elliptic Symbols: Theory and Applications

Wave Factorization of Elliptic Symbols: Theory and Applications
Title Wave Factorization of Elliptic Symbols: Theory and Applications PDF eBook
Author Vladimir B. Vasil'ev
Publisher Springer Science & Business Media
Pages 192
Release 2000-09-30
Genre Mathematics
ISBN 9780792365310

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This monograph is devoted to the development of a new approach to studying elliptic differential and integro-differential (pseudodifferential) equations and their boundary problems in non-smooth domains. This approach is based on a special representation of symbols of elliptic operators called wave factorization. In canonical domains, for example, the angle on a plane or a wedge in space, this yields a general solution, and then leads to the statement of a boundary problem. Wave factorization has also been used to obtain explicit formulas for solving some problems in diffraction and elasticity theory. Audience: This volume will be of interest to mathematicians, engineers, and physicists whose work involves partial differential equations, integral equations, operator theory, elasticity and viscoelasticity, and electromagnetic theory. It can also be recommended as a text for graduate and postgraduate students for courses in singular integral and pseudodifferential equations.