Download or read book Elliptic Boundary Value Problems on Corner Domains written by Monique Dauge and published by Springer. This book was released on 2006-11-14 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Boundary Value Problems and Integral Equations in Nonsmooth Domains written by Martin Costabel and published by CRC Press. This book was released on 1994-10-25 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Elliptic Boundary Value Problems on Corner Domains written by Monique Dauge and published by . This book was released on 2014-09-01 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Elliptic Problems in Nonsmooth Domains written by Pierre Grisvard and published by SIAM. This book was released on 2011-10-20 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published: Boston: Pitman Advanced Pub. Program, 1985.

Download or read book Elliptic Problems in Domains with Piecewise Smooth Boundaries written by Sergey Nazarov and published by Walter de Gruyter. This book was released on 2011-06-01 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book Elliptic Boundary Value Problems in Domains with Point Singularities written by Vladimir Kozlov and published by American Mathematical Soc.. This book was released on 1997 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains written by Vladimir Maz'ya and published by Birkhäuser. This book was released on 2012-12-06 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: For the first time in the mathematical literature, this two-volume work introduces a unified and general approach to the subject. To a large extent, the book is based on the authors’ work, and has no significant overlap with other books on the theory of elliptic boundary value problems.

Download or read book Wave Factorization of Elliptic Symbols Theory and Applications written by Vladimir B. Vasil'ev and published by Springer Science & Business Media. This book was released on 2000-09-30 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Partial Differential Equations IX written by M.S. Agranovich and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: This EMS volume gives an overview of the modern theory of elliptic boundary value problems, with contributions focusing on differential elliptic boundary problems and their spectral properties, elliptic pseudodifferential operators, and general differential elliptic boundary value problems in domains with singularities.

Download or read book Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains Volume II written by Vladimir Maz'ya and published by Birkhäuser. This book was released on 2012-12-06 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: For the first time in the mathematical literature, this two-volume work introduces a unified and general approach to the subject. To a large extent, the book is based on the authors’ work, and has no significant overlap with other books on the theory of elliptic boundary value problems

Download or read book Numerical Approximation Methods for Elliptic Boundary Value Problems written by Olaf Steinbach and published by Springer Science & Business Media. This book was released on 2007-12-22 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a unified theory of the Finite Element Method and the Boundary Element Method for a numerical solution of second order elliptic boundary value problems. This includes the solvability, stability, and error analysis as well as efficient methods to solve the resulting linear systems. Applications are the potential equation, the system of linear elastostatics and the Stokes system. While there are textbooks on the finite element method, this is one of the first books on Theory of Boundary Element Methods. It is suitable for self study and exercises are included.

Download or read book Elliptic Boundary Value Problems of Second Order in Piecewise Smooth Domains written by Michail Borsuk and published by Elsevier. This book was released on 2006-01-12 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book contains a systematic treatment of the qualitative theory of elliptic boundary value problems for linear and quasilinear second order equations in non-smooth domains. The authors concentrate on the following fundamental results: sharp estimates for strong and weak solutions, solvability of the boundary value problems, regularity assertions for solutions near singular points.Key features:* New the Hardy – Friedrichs – Wirtinger type inequalities as well as new integral inequalities related to the Cauchy problem for a differential equation.* Precise exponents of the solution decreasing rate near boundary singular points and best possible conditions for this.* The question about the influence of the coefficients smoothness on the regularity of solutions.* New existence theorems for the Dirichlet problem for linear and quasilinear equations in domains with conical points.* The precise power modulus of continuity at singular boundary point for solutions of the Dirichlet, mixed and the Robin problems.* The behaviour of weak solutions near conical point for the Dirichlet problem for m – Laplacian.* The behaviour of weak solutions near a boundary edge for the Dirichlet and mixed problem for elliptic quasilinear equations with triple degeneration.* Precise exponents of the solution decreasing rate near boundary singular points and best possible conditions for this.* The question about the influence of the coefficients smoothness on the regularity of solutions.* New existence theorems for the Dirichlet problem for linear and quasilinear equations in domains with conical points.* The precise power modulus of continuity at singular boundary point for solutions of the Dirichlet, mixed and the Robin problems.* The behaviour of weak solutions near conical point for the Dirichlet problem for m - Laplacian.* The behaviour of weak solutions near a boundary edge for the Dirichlet and mixed problem for elliptic quasilinear equations with triple degeneration.

Download or read book Strongly Elliptic Systems and Boundary Integral Equations written by William Charles Hector McLean and published by Cambridge University Press. This book was released on 2000-01-28 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2000 book provided the first detailed exposition of the mathematical theory of boundary integral equations of the first kind on non-smooth domains.

Download or read book Polyharmonic Boundary Value Problems written by Filippo Gazzola and published by Springer. This book was released on 2010-05-26 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: This accessible monograph covers higher order linear and nonlinear elliptic boundary value problems in bounded domains, mainly with the biharmonic or poly-harmonic operator as leading principal part. It provides rapid access to recent results and references.

Download or read book Numerical Methods for Elliptic and Parabolic Partial Differential Equations written by Peter Knabner and published by Springer Science & Business Media. This book was released on 2003-06-26 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text provides an application oriented introduction to the numerical methods for partial differential equations. It covers finite difference, finite element, and finite volume methods, interweaving theory and applications throughout. The book examines modern topics such as adaptive methods, multilevel methods, and methods for convection-dominated problems and includes detailed illustrations and extensive exercises.

Download or read book Singularities in Elliptic Boundary Value Problems and Elasticity and Their Connection with Failure Initiation written by Zohar Yosibash and published by Springer Science & Business Media. This book was released on 2011-12-02 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introductory and self-contained book gathers as much explicit mathematical results on the linear-elastic and heat-conduction solutions in the neighborhood of singular points in two-dimensional domains, and singular edges and vertices in three-dimensional domains. These are presented in an engineering terminology for practical usage. The author treats the mathematical formulations from an engineering viewpoint and presents high-order finite-element methods for the computation of singular solutions in isotropic and anisotropic materials, and multi-material interfaces. The proper interpretation of the results in engineering practice is advocated, so that the computed data can be correlated to experimental observations. The book is divided into fourteen chapters, each containing several sections. Most of it (the first nine Chapters) addresses two-dimensional domains, where only singular points exist. The solution in a vicinity of these points admits an asymptotic expansion composed of eigenpairs and associated generalized flux/stress intensity factors (GFIFs/GSIFs), which are being computed analytically when possible or by finite element methods otherwise. Singular points associated with weakly coupled thermoelasticity in the vicinity of singularities are also addressed and thermal GSIFs are computed. The computed data is important in engineering practice for predicting failure initiation in brittle material on a daily basis. Several failure laws for two-dimensional domains with V-notches are presented and their validity is examined by comparison to experimental observations. A sufficient simple and reliable condition for predicting failure initiation (crack formation) in micron level electronic devices, involving singular points, is still a topic of active research and interest, and is addressed herein. Explicit singular solutions in the vicinity of vertices and edges in three-dimensional domains are provided in the remaining five chapters. New methods for the computation of generalized edge flux/stress intensity functions along singular edges are presented and demonstrated by several example problems from the field of fracture mechanics; including anisotropic domains and bimaterial interfaces. Circular edges are also presented and the author concludes with some remarks on open questions. This well illustrated book will appeal to both applied mathematicians and engineers working in the field of fracture mechanics and singularities.

Download or read book Elliptic Equations in Polyhedral Domains written by V. G. Maz_i_a and published by American Mathematical Soc.. This book was released on 2010-04-22 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first monograph which systematically treats elliptic boundary value problems in domains of polyhedral type. The authors mainly describe their own recent results focusing on the Dirichlet problem for linear strongly elliptic systems of arbitrary order, Neumann and mixed boundary value problems for second order systems, and on boundary value problems for the stationary Stokes and Navier-Stokes systems. A feature of the book is the systematic use of Green's matrices. Using estimates for the elements of these matrices, the authors obtain solvability and regularity theorems for the solutions in weighted and non-weighted Sobolev and Holder spaces. Some classical problems of mathematical physics (Laplace and biharmonic equations, Lame system) are considered as examples. Furthermore, the book contains maximum modulus estimates for the solutions and their derivatives. The exposition is self-contained, and an introductory chapter provides background material on the theory of elliptic boundary value problems in domains with smooth boundaries and in domains with conical points. The book is destined for graduate students and researchers working in elliptic partial differential equations and applications.