Variational Problems With Concentration
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Variational Problems With Concentration
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Author : Martin F. Bach
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Variational Problems With Concentration written by Martin F. Bach and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
To start with we describe two applications of the theory to be developed in this monograph: Bernoulli's free-boundary problem and the plasma problem. Bernoulli's free-boundary problem This problem arises in electrostatics, fluid dynamics, optimal insulation, and electro chemistry. In electrostatic terms the task is to design an annular con denser consisting of a prescribed conducting surface 80. and an unknown conduc tor A such that the electric field 'Vu is constant in magnitude on the surface 8A of the second conductor (Figure 1.1). This leads to the following free-boundary problem for the electric potential u. -~u 0 in 0. \A, u 0 on 80., u 1 on 8A, 8u Q on 8A. 811 The unknowns are the free boundary 8A and the potential u. In optimal in sulation problems the domain 0. \ A represents the insulation layer. Given the exterior boundary 80. the problem is to design an insulating layer 0. \ A of given volume which minimizes the heat or current leakage from A to the environment ]R.n \ n. The heat leakage per unit time is the capacity of the set A with respect to n. Thus we seek to minimize the capacity among all sets A c 0. of equal volume.
Variational Problems With Concentration
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Author : Martin F. Bach
language : en
Publisher: Birkhäuser
Release Date : 2012-11-02
Variational Problems With Concentration written by Martin F. Bach and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-02 with Mathematics categories.
This self-contained research monograph focuses on semilinear Dirichlet problems and similar equations involving the p-Laplacian. The author explains new techniques in detail, and derives several numerical methods approximating the concentration point and the free boundary. The corresponding plots are highlights of this book.
Lagrange Multiplier Approach To Variational Problems And Applications
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Author : Kazufumi Ito
language : en
Publisher: SIAM
Release Date : 2008-01-01
Lagrange Multiplier Approach To Variational Problems And Applications written by Kazufumi Ito and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-01 with Mathematics categories.
Lagrange multiplier theory provides a tool for the analysis of a general class of nonlinear variational problems and is the basis for developing efficient and powerful iterative methods for solving these problems. This comprehensive monograph analyzes Lagrange multiplier theory and shows its impact on the development of numerical algorithms for problems posed in a function space setting. The authors develop and analyze efficient algorithms for constrained optimization and convex optimization problems based on the augumented Lagrangian concept and cover such topics as sensitivity analysis, convex optimization, second order methods, and shape sensitivity calculus. General theory is applied to challenging problems in optimal control of partial differential equations, image analysis, mechanical contact and friction problems, and American options for the Black-Scholes model.
Noncoercive Variational Problems And Related Results
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Author : Daniel Goeleven
language : en
Publisher: CRC Press
Release Date : 1996-10-10
Noncoercive Variational Problems And Related Results written by Daniel Goeleven and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-10-10 with Mathematics categories.
In establishing a general theory of the existence of solutions for noncoercive variational problems and constrained problems formulated as variational inequalities or hemivariational inequalities, this Research Note illustrates recent mathematical approaches and results with various examples from mathematics and mechanics. The book unifies ideas for the treatment of various noncoercive problems and provides previously unpublished results for variational inequalities and hemivariational inequalities. The author points out important applications in mechanics and their mathfematical tratment using recession tools. This book will be of particular interest to researchers in pure and aplied mathematics and mechanics.
Introduction To Numerical Methods For Variational Problems
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Author : Hans Petter Langtangen
language : en
Publisher: Springer Nature
Release Date : 2019-09-26
Introduction To Numerical Methods For Variational Problems written by Hans Petter Langtangen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-26 with Mathematics categories.
This textbook teaches finite element methods from a computational point of view. It focuses on how to develop flexible computer programs with Python, a programming language in which a combination of symbolic and numerical tools is used to achieve an explicit and practical derivation of finite element algorithms. The finite element library FEniCS is used throughout the book, but the content is provided in sufficient detail to ensure that students with less mathematical background or mixed programming-language experience will equally benefit. All program examples are available on the Internet.
Convex Variational Problems
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Author : Michael Bildhauer
language : en
Publisher: Springer
Release Date : 2003-01-01
Convex Variational Problems written by Michael Bildhauer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-01 with Mathematics categories.
The author emphasizes a non-uniform ellipticity condition as the main approach to regularity theory for solutions of convex variational problems with different types of non-standard growth conditions. This volume first focuses on elliptic variational problems with linear growth conditions. Here the notion of a "solution" is not obvious and the point of view has to be changed several times in order to get some deeper insight. Then the smoothness properties of solutions to convex anisotropic variational problems with superlinear growth are studied. In spite of the fundamental differences, a non-uniform ellipticity condition serves as the main tool towards a unified view of the regularity theory for both kinds of problems.
Lectures On Geometric Variational Problems
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Author : Seiki Nishikawa
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Lectures On Geometric Variational Problems written by Seiki Nishikawa 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 2012-12-06 with Mathematics categories.
In this volume are collected notes of lectures delivered at the First In ternational Research Institute of the Mathematical Society of Japan. This conference, held at Tohoku University in July 1993, was devoted to geometry and global analysis. Subsequent to the conference, in answer to popular de mand from the participants, it was decided to publish the notes of the survey lectures. Written by the lecturers themselves, all experts in their respective fields, these notes are here presented in a single volume. It is hoped that they will provide a vivid account of the current research, from the introduc tory level up to and including the most recent results, and will indicate the direction to be taken by future researeh. This compilation begins with Jean-Pierre Bourguignon's notes entitled "An Introduction to Geometric Variational Problems," illustrating the gen eral framework of the field with many examples and providing the reader with a broad view of the current research. Following this, Kenji Fukaya's notes on "Geometry of Gauge Fields" are concerned with gauge theory and its applications to low-dimensional topology, without delving too deeply into technical detail. Special emphasis is placed on explaining the ideas of infi nite dimensional geometry that, in the literature, are often hidden behind rigorous formulations or technical arguments.
Concentration Compactness
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Author : Kyril Tintarev
language : en
Publisher: Imperial College Press
Release Date : 2007
Concentration Compactness written by Kyril Tintarev and has been published by Imperial College Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
Concentration compactness is an important method in mathematical analysis which has been widely used in mathematical research for two decades. This unique volume fulfills the need for a source book that usefully combines a concise formulation of the method, a range of important applications to variational problems, and background material concerning manifolds, non-compact transformation groups and functional spaces. Highlighting the role in functional analysis of invariance and, in particular, of non-compact transformation groups, the book uses the same building blocks, such as partitions of domain and partitions of range, relative to transformation groups, in the proofs of energy inequalities and in the weak convergence lemmas.
Variational Methods In Shape Optimization Problems
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Author : Dorin Bucur
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-09-13
Variational Methods In Shape Optimization Problems written by Dorin Bucur 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 2006-09-13 with Mathematics categories.
Shape optimization problems are treated from the classical and modern perspectives Targets a broad audience of graduate students in pure and applied mathematics, as well as engineers requiring a solid mathematical basis for the solution of practical problems Requires only a standard knowledge in the calculus of variations, differential equations, and functional analysis Driven by several good examples and illustrations Poses some open questions.
Nonsmooth Variational Problems And Their Inequalities
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Author : Siegfried Carl
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-07
Nonsmooth Variational Problems And Their Inequalities written by Siegfried Carl 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 2007-06-07 with Mathematics categories.
This monograph focuses primarily on nonsmooth variational problems that arise from boundary value problems with nonsmooth data and/or nonsmooth constraints, such as multivalued elliptic problems, variational inequalities, hemivariational inequalities, and their corresponding evolution problems. It provides a systematic and unified exposition of comparison principles based on a suitably extended sub-supersolution method.