Variational Analysis in Sobolev and BV Spaces: Applications to PDEs and Optimization (MPS-SIAM Series on Optimization)

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This self-contained book is excellent for graduate-level courses devoted to variational analysis, optimization, and partial differential equations (PDEs). It provides readers with a complete guide to problems in these fields as well as a detailed presentation of the most important tools and methods of variational analysis. New trends in variational analysis are also presented, along with recent developments and applications in this area. Variational Analysis in Sobolev and BV Spaces: Applications to PDEs and Optimization is not just for students, however; it is a comprehensive guide for anyone who wants to approach the field of variational analysis in a systematic way, starting from the most classical examples and working up to a research level. This book also contains several applications to problems in geometry, mechanics, elasticity, and computer vision, along with a complete list of references. Organized in a way that makes it accessible to a large audience, the book is divided into two parts. In Part I, classical Sobolev spaces are introduced and the reader is provided with the basic tools and methods of variational analysis and optimization in infinite dimensional spaces, with applications to classical PDE problems. The last chapters in Part I introduce finite element methods and spectral analysis methods, the two most powerful tools that allow the computation of approximate solutions of variational problems. In Part II, BV(W) spaces are introduced and new trends in variational analysis are presented. In this part the reader is introduced to the flexibility of variational methods.

Variational Methods for Potential Operator Equations: With Applications to Nonlinear Elliptic Equations (De Gruyter Studies in Mathematics)

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Variational Methods for Potential Operator Equations: With Applications to Nonlinear Elliptic Equations (De Gruyter Studies in Mathematics)
Jan Chabrowski
Manufacturer: Walter de Gruyter
ProductGroup: Book
Binding: Hardcover

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ASIN: 311015269X

Variational Methods: Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems (Ergebnisse der Mathematik und ihrer Grenzgebiete. ... / A Series of Modern Surveys in Mathematics)

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Variational Methods: Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems (Ergebnisse der Mathematik und ihrer Grenzgebiete. ... / A Series of Modern Surveys in Mathematics)
Michael Struwe
Manufacturer: Springer
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Binding: Hardcover

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ASIN: 3540664793

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Hilbert's talk at the second International Congress of 1900 in Paris marked the beginning of a new era in the calculus of variations. A development began which, within a few decades, brought tremendous success, highlighted by the 1929 theorem of Ljusternik and Schnirelman on the existence of three distinct prime closed geodesics on any compact surface of genus zero, and the 1930/31 solution of Plateau's problem by Douglas and Radó. The book gives a concise introduction to variational methods and presents an overview of areas of current research in the field. The third edition gives a survey on new developments in the field. References have been updated and a small number of mistakes have been rectified.

Variational Methods in Shape Optimization Problems (Progress in Nonlinear Differential Equations and Their Applications)

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Variational Methods in Shape Optimization Problems (Progress in Nonlinear Differential Equations and Their Applications)
Dorin Bucur , and Giuseppe Buttazzo
Manufacturer: Birkhäuser Boston
ProductGroup: Book
Binding: Hardcover

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ASIN: 0817643591

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The study of shape optimization problems encompasses a wide spectrum of academic research with numerous applications to the real world. In this work these problems are treated from both the classical and modern perspectives and target 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.

Key topics and features:

* Presents foundational introduction to shape optimization theory

* Studies certain classical problems: the isoperimetric problem and the Newton problem involving the best aerodynamical shape, and optimization problems over classes of convex domains

* Treats optimal control problems under a general scheme, giving a topological framework, a survey of "gamma"-convergence, and problems governed by ODE

* Examines shape optimization problems with Dirichlet and Neumann conditions on the free boundary, along with the existence of classical solutions

* Studies optimization problems for obstacles and eigenvalues of elliptic operators

* Poses several open problems for further research

* Substantial bibliography and index

Driven by good examples and illustrations and requiring only a standard knowledge in the calculus of variations, differential equations, and functional analysis, the book can serve as a text for a graduate course in computational methods of optimal design and optimization, as well as an excellent reference for applied mathematicians addressing functional shape optimization problems.

Elliptic Boundary Value Problems with Indefinite Weights, Variational Formulations of the Principal Eigenvalue, and Applications (Research Notes in Mathematics Series)

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Elliptic Boundary Value Problems with Indefinite Weights, Variational Formulations of the Principal Eigenvalue, and Applications (Research Notes in Mathematics Series)
Fethi Belgacem
Manufacturer: Chapman & Hall/CRC
ProductGroup: Book
Binding: Paperback

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Elliptic Boundary Value Problems With Indefinite Weights presents a unified approach to the methodologies dealing with eigenvalue problems involving indefinite weights. The principal eigenvalue for such problems is characterized for various boundary conditions. Such characterizations are used, in particular, to formulate criteria for the persistence and extinctions of populations, and applications of the formulations obtained can be quite extensive.

Nonlinear Functional Analysis and Its Applications: Part 3: Variational Methods and Optimization

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Nonlinear Functional Analysis and Its Applications: Part 3: Variational Methods and Optimization
E. Zeidler
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 038790915X

Convex analysis and variational problems (Studies in mathematics and its applications)

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Convex analysis and variational problems (Studies in mathematics and its applications)
I Ekeland
Manufacturer: distributors for the U.S.A., American Elsevier Pub. Co
ProductGroup: Book
Binding: Unknown Binding

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ASIN: 044410898X

Book Description

No one working in duality should be without a copy of Convex Analysis and Variational Problems. This book contains different developments of infinite dimensional convex programming in the context of convex analysis, including duality, minmax and Lagrangians, and convexification of nonconvex optimization problems in the calculus of variations (infinite dimension). It also includes the theory of convex duality applied to partial differential equations; no other reference presents this in a systematic way. The minmax theorems contained in this book have many useful applications, in particular the robust control of partial differential equations in finite time horizon. First published in English in 1976, this SIAM Classics in Applied Mathematics edition contains the original text along with a new preface and some additional references.

Duality in Optimization and Variational Inequalities (Optimization Theory & Applications)

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Duality in Optimization and Variational Inequalities (Optimization Theory & Applications)
C.j. Goh
Manufacturer: Taylor & Francis
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Binding: Hardcover

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ASIN: 0415274796

Book Description

This comprehensive volume covers a wide range of duality topics ranging from simple ideas in network flows to complex issues in non-convex optimization and multicriteria problems. In addition, it examines duality in the context of variational inequalities and vector variational inequalities, as generalizations to optimization. Duality in Optimization and Variational Inequalities is intended for researchers and practitioners of optimization with the aim of enhancing their understanding of duality. It provides a wider appreciation of optimality conditions in various scenarios and under different assumptions. It will enable the reader to use duality to devise more effective computational methods, and to aid more meaningful interpretation of optimization and variational inequality problems.

Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models (Nonconvex Optimization and Its Applications)

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Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models (Nonconvex Optimization and Its Applications)

Manufacturer: Springer
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Binding: Hardcover

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ASIN: 1402001614

Book Description

The aim of the book is to cover the three fundamental aspects of research in equilibrium problems: the statement problem and its formulation using mainly variational methods, its theoretical solution by means of classical and new variational tools, the calculus of solutions and applications in concrete cases. The book shows how many equilibrium problems follow a general law (the so-called user equilibrium condition). Such law allows us to express the problem in terms of variational inequalities. Variational inequalities provide a powerful methodology, by which existence and calculation of the solution can be obtained.

Geometrical Methods in Variational Problems (Mathematics and Its Applications)

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Geometrical Methods in Variational Problems (Mathematics and Its Applications)
N.A. Bobylov , S.V. Emel'yanov , and S. Korovin
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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This self-contained monograph presents methods for the investigation of nonlinear variational problems. These methods are based on geometric and topological ideas such as topological index, degree of a mapping, Morse-Conley index, Euler characteristics, deformation invariant, homotopic invariant, and the Lusternik-Shnirelman category. Attention is also given to applications in optimisation, mathematical physics, control, and numerical methods.

Audience: This volume will be of interest to specialists in functional analysis and its applications, and can also be recommended as a text for graduate and postgraduate-level courses in these fields.

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'Secret History' is a favorite work by one of my favorite authors.

A perverse Samurai Lord and a nostalgic trip to a mountain village

Remember, these are novels...

An obsession with noseless heads.

The Secret History of the Lord of Musashi and Arrowroot: Two Novels
Junichiro Tanizaki , and Anthony H. Chambers
Manufacturer: Vintage
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Binding: Paperback

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Seven Japanese Tales

The Key & Diary of a Mad Old Man

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The Makioka Sisters

The Reed Cutter and Captain Shigemoto's Mother: Two Novellas

ASIN: 0375719318
Release Date: 2003-03-11

Book Description

From a Japanese master of romantic and sexual obsession come two novels that treat traditional themes with sly wit and startling psychological sophistication. In The Secret History of the Lord of Musashi, Junichir Tanizaki reimagines the exploits of a legendary samurai as a sadomasochistic dance between the hero and the wife of his enemy. Arrowroot, though set in the twentieth century, views an adult orphan’s search for his mother’s past through the translucent shoji screen of ancient literature and myth.

Both works are replete with shocking juxtapositions. Severed heads become objects of erotic fixation. Foxes take on human shape. An aristocratic lady loves and pities the man she is conspiring to destroy. This supple translation reveals the full scope of Tanizaki’s gift: his confident storytelling, luminous detail, and astonishingly vital female characters.

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'Secret History' is a favorite work by one of my favorite authors........2007-05-27

And as fine a piece of dreamy writing as 'Arrowroot' is, the melding in the former of Tanizaki's detail-gilded historical tales with his darkly comic studies of sexual obsession makes for a heady brew indeed! (It has a breakneck page-turner quality that contrasts nicely with the more languidly paced 'Arrowroot.') As always, his prose is a pleasure to read, even in translation. I would rank that story with his exquisite long novel 'Sasame Yuki.' Very highly recommended.

A perverse Samurai Lord and a nostalgic trip to a mountain village.......2005-09-11

Junichiro Tanizaki is often a complicated, perverse author. He delves into the mysterious realm of sexual fetishism and body horror, presenting grotesqueries in a uniquely straight-forward writing style that is itself neither fetishistic nor perverse, lending an air of normalcy to the bizarre figures that populate his tales. At the same time, he can write sensitive, beautiful stories without a hint of sexual exploration.

Taking a similar theme in two very different directions, "The Secret History of the Lord of Musashi/Arrowroot" showcases these two sides of Tanizaki's talent. Both deal with "books within a book," using this device as a launching point for the narrative. One is a dark tale of body horror and sexual perversion, and the other is a simple piece of nostalgia. The two stories were said to be the author's favorites.

"The Secret History of the Lord of Musashi" revolves around a fictional Samurai lord, and two fictional "re-discovered texts" that detail the secret sexual life of the Lord of Musashi. From the two books, The Dream of a Night and Memiors of Doamai, the narrator pieces together the cruel pleasures of a man obsessed with nose-less severed heads. In his young boyhood, he watched the women washing the severed heads of defeated Samurai and experienced his first sexual desire while watching their beautiful fingers manipulating the grotesque objects. Unquenched bye the passing years, his fetish leads him to an affair with the passionately cruel Lady Kikyo, who's father's nose he severed as a boy. Finally, his own marriage is encountered, and the abuse of his servant Doamai.

The writing style, using an almost lectural tone of one giving a class on the life of the Lord of Musashi, softens the impact of the horror of using severed heads as sexual aids. It is a very interesting story, in the true Tanizaki style.

"Arrowroot" is much shorter, and is set in the hidden mountains of Yoshino, in Nara prefecture. Two friends take a trip to the mountains, under the premise of going to see a fabled drum in the possession of a small village family. The author thinks of the trip as research into a possible historical novel detailing the Southern Court, while his friend has a secret motive. The story is very beautifully written, sensitive and nostalgic. It is a complete reversal from "The Secret History of the Lord of Musashi" and yet is somehow a perfect companion.

Remember, these are novels..........2000-06-24

This books contains two novellas by Junichiro Tanizaki and tranlated by Anthony Chambers. Tanizaki wrote these in 1930 and they are suppose to be his favorite.

The Secret History of the Lord of Musashi is filled with scandel. The subject is of a great lord whose sexual fixations includes a sick obsession in severed heads, espcially those without noses. This is more of a horror story of old.

Arrowroot is meditative, poetic, it describes the journey of two friends traveling together. One is looking for information about a lost imperial court from the 15th centuary, the other is trying to understand his dead mother.

An obsession with noseless heads........1997-06-18

The Secret History of the Lord of Musashi is a masterpiece of dysfunction. A lord who becomes obsessed with 'woman heads,' noseless heads collected at the ends of mighty battles. The samurai are to collect the heads of fallen foes during battle, but the more kills, the harder it is to carry all the heads, so instead they take noses, and it is the job of a group of women to fit the noses back onto the voided faces. It is this ritual the young Lord of Musashi comes across, and the rest makes for a great read!

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