Variational Problems In Transport Theory With Mass Concentration
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Variational Problems In Transport Theory With Mass Concentration
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Author : Filippo Santambrogio
language : en
Publisher: Edizioni della Normale
Release Date : 2007-12-13
Variational Problems In Transport Theory With Mass Concentration written by Filippo Santambrogio and has been published by Edizioni della Normale this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-13 with Mathematics categories.
This book examines variational problems involving optimal transportation of probability measures, in competition with concentration effects. It presents some problems where measures have to be selected minimizing transport costs between them, but satisfying some concentration criteria, with possible applications to urban planning. The book also covers optimization problems where the concentration or diffusion phenomena occurs directly at the level of the transportation structure.
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.
Optimal Transportation And Applications
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Author : Luigi Ambrosio
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-06-12
Optimal Transportation And Applications 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 2003-06-12 with Mathematics categories.
Leading researchers in the field of Optimal Transportation, with different views and perspectives, contribute to this Summer School volume: Monge-Ampère and Monge-Kantorovich theory, shape optimization and mass transportation are linked, among others, to applications in fluid mechanics granular material physics and statistical mechanics, emphasizing the attractiveness of the subject from both a theoretical and applied point of view. The volume is designed to become a guide to researchers willing to enter into this challenging and useful theory.
Regularity Of Optimal Transport Maps And Applications
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Author : Guido Philippis
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-28
Regularity Of Optimal Transport Maps And Applications written by Guido Philippis 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 2013-06-28 with Mathematics categories.
In this thesis, we study the regularity of optimal transport maps and its applications to the semi-geostrophic system. The first two chapters survey the known theory, in particular there is a self-contained proof of Brenier’ theorem on existence of optimal transport maps and of Caffarelli’s Theorem on Holder continuity of optimal maps. In the third and fourth chapter we start investigating Sobolev regularity of optimal transport maps, while in Chapter 5 we show how the above mentioned results allows to prove the existence of Eulerian solution to the semi-geostrophic equation. In Chapter 6 we prove partial regularity of optimal maps with respect to a generic cost functions (it is well known that in this case global regularity can not be expected). More precisely we show that if the target and source measure have smooth densities the optimal map is always smooth outside a closed set of measure zero.
Some Optimization Problems In Mass Transport Theory
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Author : Serena Lo Bianco Guarino
language : en
Publisher:
Release Date : 2014
Some Optimization Problems In Mass Transport Theory written by Serena Lo Bianco Guarino and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with categories.
Optimal Transport
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Author : Cédric Villani
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-10-26
Optimal Transport written by Cédric Villani 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 2008-10-26 with Mathematics categories.
At the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and John Mather launched a revolution in the venerable field of optimal transport founded by G. Monge in the 18th century, which has made breathtaking forays into various other domains of mathematics ever since. The author presents a broad overview of this area, supplying complete and self-contained proofs of all the fundamental results of the theory of optimal transport at the appropriate level of generality. Thus, the book encompasses the broad spectrum ranging from basic theory to the most recent research results. PhD students or researchers can read the entire book without any prior knowledge of the field. A comprehensive bibliography with notes that extensively discuss the existing literature underlines the book’s value as a most welcome reference text on this subject.
Algorithms For Quadratic Matrix And Vector Equations
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Author : Federico Poloni
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-03-13
Algorithms For Quadratic Matrix And Vector Equations written by Federico Poloni 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 2012-03-13 with Mathematics categories.
This book is devoted to studying algorithms for the solution of a class of quadratic matrix and vector equations. These equations appear, in different forms, in several practical applications, especially in applied probability and control theory. The equations are first presented using a novel unifying approach; then, specific numerical methods are presented for the cases most relevant for applications, and new algorithms and theoretical results developed by the author are presented. The book focuses on “matrix multiplication-rich” iterations such as cyclic reduction and the structured doubling algorithm (SDA) and contains a variety of new research results which, as of today, are only available in articles or preprints.
Doubly Stochastic Models For Volcanic Hazard Assessment At Campi Flegrei Caldera
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Author : Andrea Bevilacqua
language : en
Publisher: Springer
Release Date : 2016-05-03
Doubly Stochastic Models For Volcanic Hazard Assessment At Campi Flegrei Caldera written by Andrea Bevilacqua and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-03 with Mathematics categories.
This study provides innovative mathematical models for assessing the eruption probability and associated volcanic hazards, and applies them to the Campi Flegrei caldera in Italy. Throughout the book, significant attention is devoted to quantifying the sources of uncertainty affecting the forecast estimates. The Campi Flegrei caldera is certainly one of the world’s highest-risk volcanoes, with more than 70 eruptions over the last 15,000 years, prevalently explosive ones of varying magnitude, intensity and vent location. In the second half of the twentieth century the volcano apparently once again entered a phase of unrest that continues to the present. Hundreds of thousands of people live inside the caldera and over a million more in the nearby city of Naples, making a future eruption of Campi Flegrei an event with potentially catastrophic consequences at the national and European levels.
Flows Of Non Smooth Vector Fields And Degenerate Elliptic Equations
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Author : Maria Colombo
language : en
Publisher: Springer
Release Date : 2017-06-07
Flows Of Non Smooth Vector Fields And Degenerate Elliptic Equations written by Maria Colombo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-07 with Mathematics categories.
The first part of the book is devoted to the transport equation for a given vector field, exploiting the lagrangian structure of solutions. It also treats the regularity of solutions of some degenerate elliptic equations, which appear in the eulerian counterpart of some transport models with congestion. The second part of the book deals with the lagrangian structure of solutions of the Vlasov-Poisson system, which describes the evolution of a system of particles under the self-induced gravitational/electrostatic field, and the existence of solutions of the semigeostrophic system, used in meteorology to describe the motion of large-scale oceanic/atmospheric flows.
Existence And Regularity Results For Some Shape Optimization Problems
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Author : Bozhidar Velichkov
language : en
Publisher: Springer
Release Date : 2015-03-21
Existence And Regularity Results For Some Shape Optimization Problems written by Bozhidar Velichkov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-21 with Mathematics categories.
We study the existence and regularity of optimal domains for functionals depending on the spectrum of the Dirichlet Laplacian or of more general Schrödinger operators. The domains are subject to perimeter and volume constraints; we also take into account the possible presence of geometric obstacles. We investigate the properties of the optimal sets and of the optimal state functions. In particular, we prove that the eigenfunctions are Lipschitz continuous up to the boundary and that the optimal sets subject to the perimeter constraint have regular free boundary. We also consider spectral optimization problems in non-Euclidean settings and optimization problems for potentials and measures, as well as multiphase and optimal partition problems.