Elliptic Boundary Value Problems On Corner Domains

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Elliptic Boundary Value Problems On Corner Domains

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Author : Monique Dauge
language : en
Publisher: Springer
Release Date : 2006-11-14

Elliptic Boundary Value Problems On Corner Domains written by Monique Dauge and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

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

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Author : Monique Dauge
language : en
Publisher:
Release Date : 2014-09-01

Elliptic Boundary Value Problems On Corner Domains written by Monique Dauge and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-01 with categories.

Elliptic Boundary Value Problems An Corner Domains Smoothness And Asymptotics Of Solutions

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Author : Monique Dauge
language : en
Publisher:
Release Date : 1988

Elliptic Boundary Value Problems An Corner Domains Smoothness And Asymptotics Of Solutions written by Monique Dauge and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Dominios con esquinas categories.

Elliptic Boundary Value Problems In Domains With Point Singularities

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Author : Vladimir Kozlov
language : en
Publisher: American Mathematical Soc.
Release Date : 1997

Elliptic Boundary Value Problems In Domains With Point Singularities written by Vladimir Kozlov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.

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

Elliptic Problems In Nonsmooth Domains

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Author : Pierre Grisvard
language : en
Publisher: SIAM
Release Date : 2011-10-20

Elliptic Problems In Nonsmooth Domains written by Pierre Grisvard and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-20 with Mathematics categories.

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

Finite Element Approximation Of Boundary Value Problems

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Author : Franz Chouly
language : en
Publisher: Springer Nature
Release Date : 2024-11-06

Finite Element Approximation Of Boundary Value Problems written by Franz Chouly and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-06 with Mathematics categories.

This textbook provides an accessible introduction to the mathematical foundations of the finite element method for a broad audience. The author accomplishes this, in part, by including numerous exercises and illustrations. Each chapter begins with a clear outline to help make complex concepts more approachable without sacrificing depth. Structurally, the book begins with the simplest type of finite element method: low order, piecewise continuous, Lagrange finite elements. With this, crucial questions about the stability and approximation errors are answered. Of particular note is the author’s coverage of two specific topics that often go overlooked in introductory material. The first is the numerical treatment of boundary conditions, especially the Nitsche technique. The second is a detailed explanation of the discretization error using specific techniques of a posteriori error estimation. With the book’s compact yet thorough treatment of these areas, readers will have a clear understanding of how mathematical analysis tools can be used in practice. Finite Element Approximation of Boundary Value Problems will be suitable as a supplementary textbook in applied mathematics courses for graduate students, and may also be used for self-study.

Partial Differential Equations Ix

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Author : M.S. Agranovich
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11

Partial Differential Equations Ix written by M.S. Agranovich and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.

This EMS volume gives an overview of the modern theory of elliptic boundary value problems. The contribution by M.S. Agranovich is devoted to differential elliptic boundary problems, mainly in smooth bounded domains, and their spectral properties. This article continues his contribution to EMS 63. The contribution by A. Brenner and E. Shargorodsky concerns the theory of boundary value problems for elliptic pseudodifferential operators. Problems both with and without the transmission property, as well as parameter-dependent problems are considered. The article by B. Plamenevskij deals with general differential elliptic boundary value problems in domains with singularities.

Boundary Value Problems And Integral Equations In Nonsmooth Domains

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Author : Martin Costabel
language : en
Publisher: CRC Press
Release Date : 1994-10-25

Boundary Value Problems And Integral Equations In Nonsmooth Domains written by Martin Costabel and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-10-25 with Mathematics categories.

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.

Singularly Perturbed Boundary Value Problems

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Author : Matteo Dalla Riva
language : en
Publisher: Springer Nature
Release Date : 2021-10-01

Singularly Perturbed Boundary Value Problems written by Matteo Dalla Riva and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-01 with Mathematics categories.

This book is devoted to the analysis of the basic boundary value problems for the Laplace equation in singularly perturbed domains. The main purpose is to illustrate a method called Functional Analytic Approach, to describe the dependence of the solutions upon a singular perturbation parameter in terms of analytic functions. Here the focus is on domains with small holes and the perturbation parameter is the size of the holes. The book is the first introduction to the topic and covers the theoretical material and its applications to a series of problems that range from simple illustrative examples to more involved research results. The Functional Analytic Approach makes constant use of the integral representation method for the solutions of boundary value problems, of Potential Theory, of the Theory of Analytic Functions both in finite and infinite dimension, and of Nonlinear Functional Analysis. Designed to serve various purposes and readerships, the extensive introductory part spanning Chapters 1–7 can be used as a reference textbook for graduate courses on classical Potential Theory and its applications to boundary value problems. The early chapters also contain results that are rarely presented in the literature and may also, therefore, attract the interest of more expert readers. The exposition moves on to introduce the Functional Analytic Approach. A reader looking for a quick introduction to the method can find simple illustrative examples specifically designed for this purpose. More expert readers will find a comprehensive presentation of the Functional Analytic Approach, which allows a comparison between the approach of the book and the more classical expansion methods of Asymptotic Analysis and offers insights on the specific features of the approach and its applications to linear and nonlinear boundary value problems.