Monge Ampere Equation: Applications to Geometry and Optimization PDF Download
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Author: Luis A. Caffarelli
Publisher: American Mathematical Soc.
ISBN: 0821809172
Category : Mathematics
Languages : en
Pages : 186
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Book Description
In recent years, the Monge Ampère Equation has received attention for its role in several new areas of applied mathematics: as a new method of discretization for evolution equations of classical mechanics, such as the Euler equation, flow in porous media, Hele-Shaw flow, etc.; as a simple model for optimal transportation and a div-curl decomposition with affine invariance; and as a model for front formation in meteorology and optimal antenna design. These applications were addressed and important theoretical advances presented at a NSF-CBMS conference held at Florida Atlantic University (Boca Raton). L. Cafarelli and other distinguished specialists contributed high-quality research results and up-to-date developments in the field. This is a comprehensive volume outlining current directions in nonlinear analysis and its applications.
Author: Luis A. Caffarelli
Publisher: American Mathematical Soc.
ISBN: 0821809172
Category : Mathematics
Languages : en
Pages : 186
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Book Description
In recent years, the Monge Ampère Equation has received attention for its role in several new areas of applied mathematics: as a new method of discretization for evolution equations of classical mechanics, such as the Euler equation, flow in porous media, Hele-Shaw flow, etc.; as a simple model for optimal transportation and a div-curl decomposition with affine invariance; and as a model for front formation in meteorology and optimal antenna design. These applications were addressed and important theoretical advances presented at a NSF-CBMS conference held at Florida Atlantic University (Boca Raton). L. Cafarelli and other distinguished specialists contributed high-quality research results and up-to-date developments in the field. This is a comprehensive volume outlining current directions in nonlinear analysis and its applications.
Author: Cristian E. Gutierrez
Publisher: Springer Science & Business Media
ISBN: 9780817641771
Category : Mathematics
Languages : en
Pages : 148
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Book Description
The Monge-Ampère equation has attracted considerable interest in recent years because of its important role in several areas of applied mathematics. Monge-Ampère 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.
Author: Andrea Bonito
Publisher: Elsevier
ISBN: 0444643060
Category : Mathematics
Languages : en
Pages : 572
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Book Description
Besides their intrinsic mathematical interest, geometric partial differential equations (PDEs) are ubiquitous in many scientific, engineering and industrial applications. They represent an intellectual challenge and have received a great deal of attention recently. The purpose of this volume is to provide a missing reference consisting of self-contained and comprehensive presentations. It includes basic ideas, analysis and applications of state-of-the-art fundamental algorithms for the approximation of geometric PDEs together with their impacts in a variety of fields within mathematics, science, and engineering. - About every aspect of computational geometric PDEs is discussed in this and a companion volume. Topics in this volume include stationary and time-dependent surface PDEs for geometric flows, large deformations of nonlinearly geometric plates and rods, level set and phase field methods and applications, free boundary problems, discrete Riemannian calculus and morphing, fully nonlinear PDEs including Monge-Ampere equations, and PDE constrained optimization - Each chapter is a complete essay at the research level but accessible to junior researchers and students. The intent is to provide a comprehensive description of algorithms and their analysis for a specific geometric PDE class, starting from basic concepts and concluding with interesting applications. Each chapter is thus useful as an introduction to a research area as well as a teaching resource, and provides numerous pointers to the literature for further reading - The authors of each chapter are world leaders in their field of expertise and skillful writers. This book is thus meant to provide an invaluable, readable and enjoyable account of computational geometric PDEs
Author: Salvador Pérez-Esteva
Publisher: American Mathematical Soc.
ISBN: 0821827081
Category : Mathematics
Languages : en
Pages : 288
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Book Description
For the second time, a Summer School in Analysis and Mathematical Physics took place at the Universidad Nacional Autonoma de Mexico in Cuernavaca. The purpose of the schools is to provide a bridge from standard graduate courses in mathematics to current research topics, particularly in analysis. The lectures are given by internationally recognized specialists in the fields. The topics covered in this Second Summer School include harmonic analysis, complex analysis, pseudodifferential operators, the mathematics of quantum chaos, and non-linear analysis.
Author: Charles N. Delzell
Publisher: American Mathematical Soc.
ISBN: 0821808044
Category : Mathematics
Languages : en
Pages : 320
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Book Description
This volume contains 16 carefully refereed articles by participants in the Special Semester and the AMS Special Session on Real Algebraic Geometry and Ordered Structures held at Louisiana State University and Southern University (Baton Rouge). The 23 contributors to this volume were among the 75 mathematicians from 15 countries who participated in the special semester. Topics include the topology of real algebraic curves (Hilbert's 16th problem), moduli of real algebraic curves, effective sums of squares of real forms (Hilbert's 17th problem), efficient real quantifier elimination, subanalytic sets and stratifications, semialgebraic singularity theory, radial vector fields, exponential functions and valuations on nonarchimedean ordered fields, valued field extensions, partially ordered and lattice-ordered rings, rings of continuous functions, spectra of rings, and abstract spaces of (higher-level) orderings and real places. This volume provides a good overview of the state of the art in this area in the 1990s. It includes both expository and original research papers by top workers in this thriving field. The authors and editors strived to make the volume useful to a wide audience (including students and researchers) interested in real algebraic geometry and ordered structures-two subjects that are obviously related, but seldom brought together.
Author: Rolf Jeltsch
Publisher: European Mathematical Society
ISBN: 9783037190562
Category : Mathematics
Languages : en
Pages : 528
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Book Description
The International Council for Industrial and Applied Mathematics (ICIAM) is the worldwide organization of societies which are dedicated primarily or significantly to applied and/or industrial mathematics. The ICIAM Congresses, held every 4 years, are run under the auspices of the Council with the aim to advance the applications of mathematics in all parts of the world. The Sixth ICIAM Congress was held in Zurich, Switzerland, July 16-20, 2007, and was attended by more than 3000 scientists from 47 countries. This volume collects the invited lectures of this Congress, the appreciations of the ICIAM Prize winners' achievements, and the Euler Lecture celebrating the 300th anniversary of Euler. The authors of these papers are leading researchers in their fields, rigorously selected by a distinguished international program committee. The book presents an overview of contemporary applications of mathematics, new perspectives, and open problems. Topics embrace analysis of and numerical methods for: linear and nonlinear partial differential equations multiscale modeling nonlinear problems involving integral operators controllability and observability asymptotic solutions of Hamilton-Jacobi equations contact problems in solid mechanics topology optimization of structures dissipation inequalities in systems theory greedy algorithms sampling in function space order-value optimization parabolic partial differential equations and deterministic games Moreover, particular applications involve risk in financial markets, radar imaging, brain dynamics, and complex geometric optics applied to acoustics and electromagnetics.
Author: Eric W. Weisstein
Publisher: CRC Press
ISBN: 1420035223
Category : Mathematics
Languages : en
Pages : 3253
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Book Description
Upon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the d
Author: Dinh Van Huynh
Publisher: American Mathematical Soc.
ISBN: 082181950X
Category : Mathematics
Languages : en
Pages : 586
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Book Description
Among all areas of mathematics, algebra is one of the best suited to find applications within the frame of our booming technological society. The thirty-eight articles in this volume encompass the proceedings of the International Conference on Algebra and Its Applications (Athens, OH, 1999), which explored the applications and interplay among the disciplines of ring theory, linear algebra, and coding theory. The presentations collected here reflect the dialogue between mathematicians involved in theoretical aspects of algebra and mathematicians involved in solving problems where state-of-the-art research tools may be used and applied. This Contemporary Mathematics series volume communicates the potential for collaboration among those interested in exploring the wealth of applications for abstract algebra in fields such as information and coding. The expository papers would serve well as supplemental reading in graduate seminars.
Author: Krzysztof Wojciechowski
Publisher: American Mathematical Soc.
ISBN: 0821820613
Category : Mathematics
Languages : en
Pages : 282
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Book Description
This collection of papers by leading researchers gives a broad picture of current research directions in geometric aspects of partial differential equations. Based on lectures presented at a Minisymposium on Spectral Invariants - Heat Equation Approach, held in September 1998 at Roskilde University in Denmark, the book provides both a careful exposition of new perspectives in classical index theory and an introduction to currently active areas of the field. Presented here are new index theorems as well as new calculations of the eta-invariant, of the spectral flow, of the Maslov index, of Seiberg-Witten monopoles, heat kernels, determinants, non-commutative residues, and of the Ray-Singer torsion. New types of boundary value problems for operators of Dirac type and generalizations to manifolds with cuspidal ends, to non-compact and to infinite-dimensional manifolds are also discussed. Throughout the book, the use of advanced analysis methods for gaining geometric insight emerges as a central theme. Aimed at graduate students and researchers, this book would be suitable as a text for an advanced graduate topics course on geometric aspects of partial differential equations and spectral invariants.
Author: Bo’az Klartag
Publisher: American Mathematical Soc.
ISBN: 1470425424
Category : Mathematics
Languages : en
Pages : 90
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Book Description
The localization technique from convex geometry is generalized to the setting of Riemannian manifolds whose Ricci curvature is bounded from below. In a nutshell, the author's method is based on the following observation: When the Ricci curvature is non-negative, log-concave measures are obtained when conditioning the Riemannian volume measure with respect to a geodesic foliation that is orthogonal to the level sets of a Lipschitz function. The Monge mass transfer problem plays an important role in the author's analysis.
