Dynamical And Geometric Aspects Of Hamilton Jacobi And Linearized Monge Amp Re Equations
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The Geometry Of Infinite Dimensional Groups
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Author : Boris Khesin
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-28
The Geometry Of Infinite Dimensional Groups written by Boris Khesin 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 2008-09-28 with Mathematics categories.
This monograph gives an overview of various classes of infinite-dimensional Lie groups and their applications in Hamiltonian mechanics, fluid dynamics, integrable systems, gauge theory, and complex geometry. The text includes many exercises and open questions.
Optimal Transport For Applied Mathematicians
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Author : Filippo Santambrogio
language : en
Publisher: Birkhäuser
Release Date : 2015-10-17
Optimal Transport For Applied Mathematicians written by Filippo Santambrogio and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-17 with Mathematics categories.
This monograph presents a rigorous mathematical introduction to optimal transport as a variational problem, its use in modeling various phenomena, and its connections with partial differential equations. Its main goal is to provide the reader with the techniques necessary to understand the current research in optimal transport and the tools which are most useful for its applications. Full proofs are used to illustrate mathematical concepts and each chapter includes a section that discusses applications of optimal transport to various areas, such as economics, finance, potential games, image processing and fluid dynamics. Several topics are covered that have never been previously in books on this subject, such as the Knothe transport, the properties of functionals on measures, the Dacorogna-Moser flow, the formulation through minimal flows with prescribed divergence formulation, the case of the supremal cost, and the most classical numerical methods. Graduate students and researchers in both pure and applied mathematics interested in the problems and applications of optimal transport will find this to be an invaluable resource.
Gradient Flows
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Author : Luigi Ambrosio
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-10-29
Gradient Flows written by Luigi Ambrosio 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 2008-10-29 with Mathematics categories.
The book is devoted to the theory of gradient flows in the general framework of metric spaces, and in the more specific setting of the space of probability measures, which provide a surprising link between optimal transportation theory and many evolutionary PDE's related to (non)linear diffusion. Particular emphasis is given to the convergence of the implicit time discretization method and to the error estimates for this discretization, extending the well established theory in Hilbert spaces. The book is split in two main parts that can be read independently of each other.
Handbook Of Nonlinear Partial Differential Equations
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Author : Andrei D. Polyanin
language : en
Publisher: CRC Press
Release Date : 2004-06-02
Handbook Of Nonlinear Partial Differential Equations written by Andrei D. Polyanin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-02 with Mathematics categories.
The Handbook of Nonlinear Partial Differential Equations is the latest in a series of acclaimed handbooks by these authors and presents exact solutions of more than 1600 nonlinear equations encountered in science and engineering--many more than any other book available. The equations include those of parabolic, hyperbolic, elliptic and other types, and the authors pay special attention to equations of general form that involve arbitrary functions. A supplement at the end of the book discusses the classical and new methods for constructing exact solutions to nonlinear equations. To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology, outline some of the methods in a schematic, simplified manner, and arrange the equations in increasing order of complexity. Highlights of the Handbook:
Comparison Geometry
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Author : Karsten Grove
language : en
Publisher: Cambridge University Press
Release Date : 1997-05-13
Comparison Geometry written by Karsten Grove and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-05-13 with Mathematics categories.
This is an up to date work on a branch of Riemannian geometry called Comparison Geometry.
Differentiable Measures And The Malliavin Calculus
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Author : Vladimir Igorevich Bogachev
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-07-21
Differentiable Measures And The Malliavin Calculus written by Vladimir Igorevich Bogachev 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 2010-07-21 with Mathematics categories.
This book provides the reader with the principal concepts and results related to differential properties of measures on infinite dimensional spaces. In the finite dimensional case such properties are described in terms of densities of measures with respect to Lebesgue measure. In the infinite dimensional case new phenomena arise. For the first time a detailed account is given of the theory of differentiable measures, initiated by S. V. Fomin in the 1960s; since then the method has found many various important applications. Differentiable properties are described for diverse concrete classes of measures arising in applications, for example, Gaussian, convex, stable, Gibbsian, and for distributions of random processes. Sobolev classes for measures on finite and infinite dimensional spaces are discussed in detail. Finally, we present the main ideas and results of the Malliavin calculus--a powerful method to study smoothness properties of the distributions of nonlinear functionals on infinite dimensional spaces with measures. The target readership includes mathematicians and physicists whose research is related to measures on infinite dimensional spaces, distributions of random processes, and differential equations in infinite dimensional spaces. The book includes an extensive bibliography on the subject.
Techniques And Applications Of Path Integration
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Author : L. S. Schulman
language : en
Publisher: Courier Corporation
Release Date : 2012-10-10
Techniques And Applications Of Path Integration written by L. S. Schulman and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-10 with Science categories.
Suitable for advanced undergraduates and graduate students, this text develops the techniques of path integration and deals with applications, covering a host of illustrative examples. 26 figures. 1981 edition.
Elementary Lie Group Analysis And Ordinary Differential Equations
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Author : Nailʹ Khaĭrullovich Ibragimov
language : en
Publisher:
Release Date : 1999
Elementary Lie Group Analysis And Ordinary Differential Equations written by Nailʹ Khaĭrullovich Ibragimov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Differential equations categories.
Handbook Of Feynman Path Integrals
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Author : Christian Grosche
language : en
Publisher: Springer
Release Date : 2013-11-13
Handbook Of Feynman Path Integrals written by Christian Grosche and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-13 with Science categories.
The Handbook of Feynman Path Integrals appears just fifty years after Richard Feynman published his pioneering paper in 1948 entitled "Space-Time Approach to Non-Relativistic Quantum Mechanics", in which he introduced his new formulation of quantum mechanics in terms of path integrals. The book presents for the first time a comprehensive table of Feynman path integrals together with an extensive list of references; it will serve the reader as a thorough introduction to the theory of path integrals. As a reference book, it is unique in its scope and will be essential for many physicists, chemists and mathematicians working in different areas of research.
The Monge Amp Re Equation
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Author : Cristian E. Gutiérrez
language : en
Publisher: Birkhauser
Release Date : 2001
The Monge Amp Re Equation written by Cristian E. Gutiérrez and has been published by Birkhauser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Monge-Ampère equations categories.
The Monge-Amp re equation has attracted considerable interest in recent years because of its important role in several areas of applied mathematics. Monge-Amp re type equations have applications in the areas of differential geometry, the calculus of variations, and several optimization problems, such as the Monge-Kantorovitch mass transfer problem. This book stresses the geometric aspects of this beautiful theory, using techniques from harmonic analysis covering lemmas and set decompositions.