Elliptic Boundary Value Problems In Domains With Point Singularities
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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.
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 Equations In Polyhedral Domains
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Author : V. G. Maz_i_a
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-04-22
Elliptic Equations In Polyhedral Domains written by V. G. Maz_i_a 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 2010-04-22 with Mathematics categories.
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.
Asymptotic Theory Of Dynamic Boundary Value Problems In Irregular Domains
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Author : Dmitrii Korikov
language : en
Publisher: Springer Nature
Release Date : 2021-04-01
Asymptotic Theory Of Dynamic Boundary Value Problems In Irregular Domains written by Dmitrii Korikov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-01 with Mathematics categories.
This book considers dynamic boundary value problems in domains with singularities of two types. The first type consists of "edges" of various dimensions on the boundary; in particular, polygons, cones, lenses, polyhedra are domains of this type. Singularities of the second type are "singularly perturbed edges" such as smoothed corners and edges and small holes. A domain with singularities of such type depends on a small parameter, whereas the boundary of the limit domain (as the parameter tends to zero) has usual edges, i.e. singularities of the first type. In the transition from the limit domain to the perturbed one, the boundary near a conical point or an edge becomes smooth, isolated singular points become small cavities, and so on. In an "irregular" domain with such singularities, problems of elastodynamics, electrodynamics and some other dynamic problems are discussed. The purpose is to describe the asymptotics of solutions near singularities of the boundary. The presented results and methods have a wide range of applications in mathematical physics and engineering. The book is addressed to specialists in mathematical physics, partial differential equations, and asymptotic methods.
Multiple Scale Analysis Of Boundary Value Problems In Thick Multi Level Junctions Of Type 3 2 2
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Author : Taras Mel'nyk
language : en
Publisher: Springer Nature
Release Date : 2020-01-03
Multiple Scale Analysis Of Boundary Value Problems In Thick Multi Level Junctions Of Type 3 2 2 written by Taras Mel'nyk and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-03 with Mathematics categories.
This book presents asymptotic methods for boundary-value problems (linear and semilinear, elliptic and parabolic) in so-called thick multi-level junctions. These complicated structures appear in a large variety of applications. A concise and readable introduction to the topic, the book provides a full review of the literature as well as a presentation of results of the authors, including the homogenization of boundary-value problems in thick multi-level junctions with non-Lipschitz boundaries, and the construction of approximations for solutions to semilinear problems. Including end-of-chapter conclusions discussing the results and their physical interpretations, this book will be of interest to researchers and graduate students in asymptotic analysis and applied mathematics as well as to physicists, chemists and engineers interested in processes such as heat and mass transfer.
Proceedings Of The St Petersburg Mathematical Society
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Author : Nina Nikolaevna Uralceva (Mathematikerin.)
language : en
Publisher: American Mathematical Soc.
Release Date :
Proceedings Of The St Petersburg Mathematical Society written by Nina Nikolaevna Uralceva (Mathematikerin.) 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 with Mathematics categories.
Proceedings Of The St Petersburg Mathematical Society
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Author : N.N. Uraltseva (Mathematikerin, Russland)
language : en
Publisher: American Mathematical Soc.
Release Date :
Proceedings Of The St Petersburg Mathematical Society written by N.N. Uraltseva (Mathematikerin, Russland) 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 with Mathematics categories.
This collection presents new results in algebra, functional analysis, and mathematical physics. In particular, evolution and spectral problems related to small motions of viscoelastic fluid are considered. Specific areas covered in the book include functional equations and functional operator equations from the point of view of the $C*$-algebraic approach, the existence of an isomorphism between certain ideals regarded as Galois modules, spectral problems in singularly perturbed domains, scattering theory, the existence of bounded solutions to the equation $\operatorname{div} u = f$ in a plane domain, and a compactification of a locally compact group. Also given is an historic overview of the mathematical seminars held at St. Petersburg State University. The results, ideas, and methods given in the book will be of interest to a broad range of specialists.
Hp Finite Element Methods For Singular Perturbations
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Author : Jens M. Melenk
language : en
Publisher: Springer
Release Date : 2004-10-19
Hp Finite Element Methods For Singular Perturbations written by Jens M. Melenk and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-19 with Mathematics categories.
Many partial differential equations arising in practice are parameter-dependent problems that are of singularly perturbed type. Prominent examples include plate and shell models for small thickness in solid mechanics, convection-diffusion problems in fluid mechanics, and equations arising in semi-conductor device modelling. Common features of these problems are layers and, in the case of non-smooth geometries, corner singularities. Mesh design principles for the efficient approximation of both features by the hp-version of the finite element method (hp-FEM) are proposed in this volume. For a class of singularly perturbed problems on polygonal domains, robust exponential convergence of the hp-FEM based on these mesh design principles is established rigorously.
Asymptotic Formulae In Spectral Geometry
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Author : Peter B. Gilkey
language : en
Publisher: CRC Press
Release Date : 2003-12-17
Asymptotic Formulae In Spectral Geometry written by Peter B. Gilkey and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-12-17 with Mathematics categories.
A great deal of progress has been made recently in the field of asymptotic formulas that arise in the theory of Dirac and Laplace type operators. Asymptotic Formulae in Spectral Geometry collects these results and computations into one book. Written by a leading pioneer in the field, it focuses on the functorial and special cases methods of computing asymptotic heat trace and heat content coefficients in the heat equation. It incorporates the work of many authors into the presentation, and includes a complete bibliography that serves as a roadmap to the literature on the subject. Geometers, mathematical physicists, and analysts alike will undoubtedly find this book to be the definitive book on the subject