Variational Principles in Mathematical Physics, Geometry, and Economics

Qualitative Analysis of Nonlinear Equations and Unilateral Problems
Author: Alexandru Kristály,Vicenţiu D. Rădulescu,Csaba Varga
Publisher: Cambridge University Press
ISBN: 0521117828
Category: Mathematics
Page: 368
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A comprehensive introduction to modern applied functional analysis. Assumes only basic notions of calculus, real analysis, geometry, and differential equations.

Variational Methods

In Imaging and Geometric Control
Author: Maitine Bergounioux,Gabriel Peyré,Christoph Schnörr,Jean-Baptiste Caillau,Thomas Haberkorn
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110430398
Category: Mathematics
Page: 540
View: 5751

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With a focus on the interplay between mathematics and applications of imaging, the first part covers topics from optimization, inverse problems and shape spaces to computer vision and computational anatomy. The second part is geared towards geometric control and related topics, including Riemannian geometry, celestial mechanics and quantum control. Contents: Part I Second-order decomposition model for image processing: numerical experimentation Optimizing spatial and tonal data for PDE-based inpainting Image registration using phase・amplitude separation Rotation invariance in exemplar-based image inpainting Convective regularization for optical flow A variational method for quantitative photoacoustic tomography with piecewise constant coefficients On optical flow models for variational motion estimation Bilevel approaches for learning of variational imaging models Part II Non-degenerate forms of the generalized Euler・Lagrange condition for state-constrained optimal control problems The Purcell three-link swimmer: some geometric and numerical aspects related to periodic optimal controls Controllability of Keplerian motion with low-thrust control systems Higher variational equation techniques for the integrability of homogeneous potentials Introduction to KAM theory with a view to celestial mechanics Invariants of contact sub-pseudo-Riemannian structures and Einstein・Weyl geometry Time-optimal control for a perturbed Brockett integrator Twist maps and Arnold diffusion for diffeomorphisms A Hamiltonian approach to sufficiency in optimal control with minimal regularity conditions: Part I Index

Algebraic and Geometric Methods in Nonlinear Control Theory


Author: M. Fliess,Michiel Hazewinkel
Publisher: Springer Science & Business Media
ISBN: 9400947062
Category: Mathematics
Page: 642
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Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point"of a Pin'. van GuIik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; ihe Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras ·are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Variational Methods in Imaging


Author: Otmar Scherzer,Markus Grasmair,Harald Grossauer,Markus Haltmeier,Frank Lenzen
Publisher: Springer Science & Business Media
ISBN: 0387692770
Category: Mathematics
Page: 320
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This book is devoted to the study of variational methods in imaging. The presentation is mathematically rigorous and covers a detailed treatment of the approach from an inverse problems point of view. Many numerical examples accompany the theory throughout the text. It is geared towards graduate students and researchers in applied mathematics. Researchers in the area of imaging science will also find this book appealing. It can serve as a main text in courses in image processing or as a supplemental text for courses on regularization and inverse problems at the graduate level.

Modern Methods in the Calculus of Variations

L^p Spaces
Author: Irene Fonseca,Giovanni Leoni
Publisher: Springer Science & Business Media
ISBN: 0387690069
Category: Science
Page: 600
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This is the first of two books on methods and techniques in the calculus of variations. Contemporary arguments are used throughout the text to streamline and present in a unified way classical results, and to provide novel contributions at the forefront of the theory. This book addresses fundamental questions related to lower semicontinuity and relaxation of functionals within the unconstrained setting, mainly in L^p spaces. It prepares the ground for the second volume where the variational treatment of functionals involving fields and their derivatives will be undertaken within the framework of Sobolev spaces. This book is self-contained. All the statements are fully justified and proved, with the exception of basic results in measure theory, which may be found in any good textbook on the subject. It also contains several exercises. Therefore,it may be used both as a graduate textbook as well as a reference text for researchers in the field. Irene Fonseca is the Mellon College of Science Professor of Mathematics and is currently the Director of the Center for Nonlinear Analysis in the Department of Mathematical Sciences at Carnegie Mellon University. Her research interests lie in the areas of continuum mechanics, calculus of variations, geometric measure theory and partial differential equations. Giovanni Leoni is also a professor in the Department of Mathematical Sciences at Carnegie Mellon University. He focuses his research on calculus of variations, partial differential equations and geometric measure theory with special emphasis on applications to problems in continuum mechanics and in materials science.

Mathematical Analysis and Its Applications

Proceedings of the International Conference on Mathematical Analysis and its Applications, Kuwait, 1985
Author: S. M. Mazhar,A. Hamoui,N. S. Faour
Publisher: Elsevier
ISBN: 1483148114
Category: Mathematics
Page: 442
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Mathematical Analysis and its Applications covers the proceedings of the International Conference on Mathematical Analysis and its Applications. The book presents studies that discuss several mathematical analysis methods and their respective applications. The text presents 38 papers that discuss topics, such as approximation of continuous functions by ultraspherical series and classes of bi-univalent functions. The representation of multipliers of eigen and joint function expansions of nonlocal spectral problems for first- and second-order differential operators is also discussed. The book will be of great interest to researchers and professionals whose work involves the use of mathematical analysis.

Variational Methods in Optimization


Author: Donald R. Smith
Publisher: Courier Corporation
ISBN: 9780486404554
Category: Mathematics
Page: 378
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Highly readable text elucidates applications of the chain rule of differentiation, integration by parts, parametric curves, line integrals, double integrals, and elementary differential equations. 1974 edition.

Differential Geometric Methods in Mathematical Physics

Proceedings of an International Conference Held at the Technical University of Clausthal, FRG, August 30 - September 2, 1983
Author: Heinz-Dietrich Doebner,Jörg-Dieter Hennig
Publisher: Springer
ISBN: 3540395857
Category: Mathematics
Page: 344
View: 6863

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Singularities in PDE and the Calculus of Variations


Author: Stanley Alama,Lia Bronsard,Peter J. Sternberg
Publisher: American Mathematical Soc.
ISBN: 9780821873311
Category: Mathematics
Page: 267
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This book contains papers presented at the "Workshop on Singularities in PDE and the Calculus of Variations" at the CRM in July 2006. The main theme of the meeting was the formation of geometrical singularities in PDE problems with a variational formulation. These equations typically arise in some applications (to physics, engineering, or biology, for example) and their resolution often requires a combination of methods coming from areas such as functional and harmonic analysis, differential geometry and geometric measure theory. Among the PDE problems discussed were: the Cahn-Hilliard model of phase transitions and domain walls; vortices in Ginzburg-Landau type models for superconductivity and superfluidity; the Ohna-Kawasaki model for di-block copolymers; models of image enhancement; and Monge-Ampere functions. The articles give a sampling of problems and methods in this diverse area of mathematics, which touches a large part of modern mathematics and its applications.

Mathematical Methods in Physics

Distributions, Hilbert Space Operators, and Variational Methods
Author: Philippe Blanchard,Erwin Bruening
Publisher: Springer Science & Business Media
ISBN: 1461200490
Category: Mathematics
Page: 471
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Physics has long been regarded as a wellspring of mathematical problems. Mathematical Methods in Physics is a self-contained presentation, driven by historic motivations, excellent examples, detailed proofs, and a focus on those parts of mathematics that are needed in more ambitious courses on quantum mechanics and classical and quantum field theory. Aimed primarily at a broad community of graduate students in mathematics, mathematical physics, physics and engineering, as well as researchers in these disciplines.

Lectures on Geometric Methods in Mathematical Physics


Author: Jerrold E. Marsden
Publisher: SIAM
ISBN: 0898711703
Category: Science
Page: 97
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A monograph on some of the ways geometry and analysis can be used in mathematical problems of physical interest. The roles of symmetry, bifurcation and Hamiltonian systems in diverse applications are explored.

Nonlinear Analysis and Variational Problems

In Honor of George Isac
Author: Panos M. Pardalos,Themistocles Rassias,Akhtar A. Khan
Publisher: Springer Science & Business Media
ISBN: 1441901582
Category: Business & Economics
Page: 490
View: 8316

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The chapters in this volume, written by international experts from different fields of mathematics, are devoted to honoring George Isac, a renowned mathematician. These contributions focus on recent developments in complementarity theory, variational principles, stability theory of functional equations, nonsmooth optimization, and several other important topics at the forefront of nonlinear analysis and optimization.

Variational Methods in Lorentzian Geometry


Author: Antonio Masiello
Publisher: CRC Press
ISBN: 9780582237995
Category: Mathematics
Page: 200
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Appliies variational methods and critical point theory on infinite dimenstional manifolds to some problems in Lorentzian geometry which have a variational nature, such as existence and multiplicity results on geodesics and relations between such geodesics and the topology of the manifold.

Topological Methods, Variational Methods and Their Applications

Taiyuan, Shan Xi, P.R. China, August 14-18, 2002
Author: Haim Br‚zis
Publisher: World Scientific
ISBN: 9812382623
Category: Mathematics
Page: 287
View: 6277

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ICM 2002 Satellite Conference on Nonlinear Analysis was held in the period: August 1418, 2002 at Taiyuan, Shanxi Province, China. This conference was organized by Mathematical School of Peking University, Academy of Mathematics and System Sciences of Chinese Academy of Sciences, Mathematical school of Nankai University, and Department of Mathematics of Shanxi University, and was sponsored by Shanxi Province Education Committee, Tian Yuan Mathematics Foundation, and Shanxi University. 166 mathematicians from 21 countries and areas in the world attended the conference. 53 invited speakers and 30 contributors presented their lectures. This conference aims at an overview of the recent development in nonlinear analysis. It covers the following topics: variational methods, topological methods, fixed point theory, bifurcations, nonlinear spectral theory, nonlinear Schrvdinger equations, semilinear elliptic equations, Hamiltonian systems, central configuration in N-body problems and variational problems arising in geometry and physics.

Variational Methods

Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems, Third Edition
Author: Michael Struwe
Publisher: Springer Science & Business Media
ISBN: 9783540664796
Category: Mathematics
Page: 274
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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 Rad??. 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 and Non-variational Methods in Nonlinear Analysis and Boundary Value Problems


Author: Dumitru Motreanu,Vicentiu D. Radulescu
Publisher: Springer Science & Business Media
ISBN: 9781402013850
Category: Mathematics
Page: 380
View: 3753

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This book reflects a significant part of authors' research activity dur ing the last ten years. The present monograph is constructed on the results obtained by the authors through their direct cooperation or due to the authors separately or in cooperation with other mathematicians. All these results fit in a unitary scheme giving the structure of this work. The book is mainly addressed to researchers and scholars in Pure and Applied Mathematics, Mechanics, Physics and Engineering. We are greatly indebted to Viorica Venera Motreanu for the careful reading of the manuscript and helpful comments on important issues. We are also grateful to our Editors of Kluwer Academic Publishers for their professional assistance. Our deepest thanks go to our numerous scientific collaborators and friends, whose work was so important for us. D. Motreanu and V. Radulescu IX Introduction The present monograph is based on original results obtained by the authors in the last decade. This book provides a comprehensive expo sition of some modern topics in nonlinear analysis with applications to the study of several classes of boundary value problems. Our framework includes multivalued elliptic problems with discontinuities, variational inequalities, hemivariational inequalities and evolution problems. The treatment relies on variational methods, monotonicity principles, topo logical arguments and optimization techniques. Excepting Sections 1 and 3 in Chapter 1 and Sections 1 and 3 in Chapter 2, the material is new in comparison with any other book, representing research topics where the authors contributed. The outline of our work is the following.