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The New Method Of Regularity Theory And Its Applications
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Book Synopsis Regularity Results for Nonlinear Elliptic Systems and Applications by : Alain Bensoussan
Download or read book Regularity Results for Nonlinear Elliptic Systems and Applications written by Alain Bensoussan and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects many helpful techniques for obtaining regularity results for solutions of nonlinear systems of partial differential equations. These are applied in various cases to provide useful examples and relevant results, particularly in such fields as fluid mechanics, solid mechanics, semiconductor theory and game theory.
Book Synopsis Regularity Theory for Mean Curvature Flow by : Klaus Ecker
Download or read book Regularity Theory for Mean Curvature Flow written by Klaus Ecker and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: * Devoted to the motion of surfaces for which the normal velocity at every point is given by the mean curvature at that point; this geometric heat flow process is called mean curvature flow. * Mean curvature flow and related geometric evolution equations are important tools in mathematics and mathematical physics.
Book Synopsis Elliptic Regularity Theory by Approximation Methods by : Edgard A. Pimentel
Download or read book Elliptic Regularity Theory by Approximation Methods written by Edgard A. Pimentel and published by Cambridge University Press. This book was released on 2022-09-29 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: A modern account of elliptic regularity theory, with a rigorous presentation of recent developments for fundamental models.
Book Synopsis Variational Analysis of Regular Mappings by : Alexander D. Ioffe
Download or read book Variational Analysis of Regular Mappings written by Alexander D. Ioffe and published by Springer. This book was released on 2017-10-26 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph offers the first systematic account of (metric) regularity theory in variational analysis. It presents new developments alongside classical results and demonstrates the power of the theory through applications to various problems in analysis and optimization theory. The origins of metric regularity theory can be traced back to a series of fundamental ideas and results of nonlinear functional analysis and global analysis centered around problems of existence and stability of solutions of nonlinear equations. In variational analysis, regularity theory goes far beyond the classical setting and is also concerned with non-differentiable and multi-valued operators. The present volume explores all basic aspects of the theory, from the most general problems for mappings between metric spaces to those connected with fairly concrete and important classes of operators acting in Banach and finite dimensional spaces. Written by a leading expert in the field, the book covers new and powerful techniques, which have proven to be highly efficient even in classical settings, and outlines the theory’s predominantly quantitative character, leading to a variety of new and unexpected applications. Variational Analysis of Regular Mappings is aimed at graduate students and researchers in nonlinear and functional analysis, especially those working in areas close to optimization and optimal control, and will be suitable to anyone interested in applying new concepts and ideas to operations research, control engineering and numerical analysis.
Book Synopsis The Oxford Handbook of Causation by : Helen Beebee
Download or read book The Oxford Handbook of Causation written by Helen Beebee and published by OUP Oxford. This book was released on 2012-01-12 with total page 816 pages. Available in PDF, EPUB and Kindle. Book excerpt: Causation is a central topic in many areas of philosophy. In metaphysics, philosophers want to know what causation is, and how it is related to laws of nature, probability, action, and freedom of the will. In epistemology, philosophers investigate how causal claims can be inferred from statistical data, and how causation is related to perception, knowledge and explanation. In the philosophy of mind, philosophers want to know whether and how the mind can be said to have causal efficacy, and in ethics, whether there is a moral distinction between acts and omissions and whether the moral value of an act can be judged according to its consequences. And causation is a contested concept in other fields of enquiry, such as biology, physics, and the law. This book provides an in-depth and comprehensive overview of these and other topics, as well as the history of the causation debate from the ancient Greeks to the logical empiricists. The chapters provide surveys of contemporary debates, while often also advancing novel and controversial claims; and each includes a comprehensive bibliography and suggestions for further reading. The book is thus the most comprehensive source of information about causation currently available, and will be invaluable for upper-level undergraduates through to professional philosophers.
Book Synopsis Nonsmooth Equations in Optimization by : Diethard Klatte
Download or read book Nonsmooth Equations in Optimization written by Diethard Klatte and published by Springer Science & Business Media. This book was released on 2005-12-17 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many questions dealing with solvability, stability and solution methods for va- ational inequalities or equilibrium, optimization and complementarity problems lead to the analysis of certain (perturbed) equations. This often requires a - formulation of the initial model being under consideration. Due to the specific of the original problem, the resulting equation is usually either not differ- tiable (even if the data of the original model are smooth), or it does not satisfy the assumptions of the classical implicit function theorem. This phenomenon is the main reason why a considerable analytical inst- ment dealing with generalized equations (i.e., with finding zeros of multivalued mappings) and nonsmooth equations (i.e., the defining functions are not c- tinuously differentiable) has been developed during the last 20 years, and that under very different viewpoints and assumptions. In this theory, the classical hypotheses of convex analysis, in particular, monotonicity and convexity, have been weakened or dropped, and the scope of possible applications seems to be quite large. Briefly, this discipline is often called nonsmooth analysis, sometimes also variational analysis. Our book fits into this discipline, however, our main intention is to develop the analytical theory in close connection with the needs of applications in optimization and related subjects. Main Topics of the Book 1. Extended analysis of Lipschitz functions and their generalized derivatives, including ”Newton maps” and regularity of multivalued mappings. 2. Principle of successive approximation under metric regularity and its - plication to implicit functions.
Book Synopsis Acta Numerica 2004: Volume 13 by : Arieh Iserles
Download or read book Acta Numerica 2004: Volume 13 written by Arieh Iserles and published by Cambridge University Press. This book was released on 2004-06-03 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: An annual volume presenting substantive survey articles in numerical mathematics and scientific computing.
Book Synopsis Nonlocal and Nonlinear Diffusions and Interactions: New Methods and Directions by : José Antonio Carrillo
Download or read book Nonlocal and Nonlinear Diffusions and Interactions: New Methods and Directions written by José Antonio Carrillo and published by Springer. This book was released on 2017-10-03 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting a selection of topics in the area of nonlocal and nonlinear diffusions, this book places a particular emphasis on new emerging subjects such as nonlocal operators in stationary and evolutionary problems and their applications, swarming models and applications to biology and mathematical physics, and nonlocal variational problems. The authors are some of the most well-known mathematicians in this innovative field, which is presently undergoing rapid development. The intended audience includes experts in elliptic and parabolic equations who are interested in extending their expertise to the nonlinear setting, as well as Ph.D. or postdoctoral students who want to enter into the most promising research topics in the field.
Book Synopsis A Course on Rough Paths by : Peter K. Friz
Download or read book A Course on Rough Paths written by Peter K. Friz and published by Springer Nature. This book was released on 2020-05-27 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: With many updates and additional exercises, the second edition of this book continues to provide readers with a gentle introduction to rough path analysis and regularity structures, theories that have yielded many new insights into the analysis of stochastic differential equations, and, most recently, stochastic partial differential equations. Rough path analysis provides the means for constructing a pathwise solution theory for stochastic differential equations which, in many respects, behaves like the theory of deterministic differential equations and permits a clean break between analytical and probabilistic arguments. Together with the theory of regularity structures, it forms a robust toolbox, allowing the recovery of many classical results without having to rely on specific probabilistic properties such as adaptedness or the martingale property. Essentially self-contained, this textbook puts the emphasis on ideas and short arguments, rather than aiming for the strongest possible statements. A typical reader will have been exposed to upper undergraduate analysis and probability courses, with little more than Itô-integration against Brownian motion required for most of the text. From the reviews of the first edition: "Can easily be used as a support for a graduate course ... Presents in an accessible way the unique point of view of two experts who themselves have largely contributed to the theory" - Fabrice Baudouin in the Mathematical Reviews "It is easy to base a graduate course on rough paths on this ... A researcher who carefully works her way through all of the exercises will have a very good impression of the current state of the art" - Nicolas Perkowski in Zentralblatt MATH
Book Synopsis Regularity Theory for Mean-Field Game Systems by : Diogo A. Gomes
Download or read book Regularity Theory for Mean-Field Game Systems written by Diogo A. Gomes and published by Springer. This book was released on 2016-09-14 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: Beginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems, including stationary and time-dependent MFGs, subquadratic and superquadratic MFG formulations, and distinct classes of mean-field couplings. It also explores stationary and time-dependent MFGs through a series of a-priori estimates for solutions of the Hamilton-Jacobi and Fokker-Planck equation. It shows sophisticated a-priori systems derived using a range of analytical techniques, and builds on previous results to explain classical solutions. The final chapter discusses the potential applications, models and natural extensions of MFGs. As MFGs connect common problems in pure mathematics, engineering, economics and data management, this book is a valuable resource for researchers and graduate students in these fields.
Book Synopsis Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques by : Leslie Ann Goldberg
Download or read book Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques written by Leslie Ann Goldberg and published by Springer Science & Business Media. This book was released on 2011-08-05 with total page 715 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the joint refereed proceedings of the 14th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2011, and the 15th International Workshop on Randomization and Computation, RANDOM 2011, held in Princeton, New Jersey, USA, in August 2011. The volume presents 29 revised full papers of the APPROX 2011 workshop, selected from 66 submissions, and 29 revised full papers of the RANDOM 2011 workshop, selected from 64 submissions. They were carefully reviewed and selected for inclusion in the book. In addition two abstracts of invited talks are included. APPROX focuses on algorithmic and complexity issues surrounding the development of efficient approximate solutions to computationally difficult problems. RANDOM is concerned with applications of randomness to computational and combinatorial problems.
Book Synopsis Agricultural Survey Methods by : Roberto Benedetti
Download or read book Agricultural Survey Methods written by Roberto Benedetti and published by John Wiley & Sons. This book was released on 2010-03-18 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: Due to the widespread use of surveys in agricultural resources estimation there is a broad and recognizable interest in methods and techniques to collect and process agricultural data. This book brings together the knowledge of academics and experts to increase the dissemination of the latest developments in agricultural statistics. Conducting a census, setting up frames and registers and using administrative data for statistical purposes are covered and issues arising from sample design and estimation, use of remote sensing, management of data quality and dissemination and analysis of survey data are explored. Key features: Brings together high quality research on agricultural statistics from experts in this field. Provides a thorough and much needed overview of developments within agricultural statistics. Contains summaries for each chapter, providing a valuable reference framework for those new to the field. Based upon a selection of key methodological papers presented at the ICAS conference series, updated and expanded to address current issues. Covers traditional statistical methodologies including sampling and weighting. This book provides a much needed guide to conducting surveys of land use and to the latest developments in agricultural statistics. Statisticians interested in agricultural statistics, agricultural statisticians in national statistics offices and statisticians and researchers using survey methodology will benefit from this book.
Book Synopsis Introduction to Numerical Continuation Methods by : Eugene L. Allgower
Download or read book Introduction to Numerical Continuation Methods written by Eugene L. Allgower and published by SIAM. This book was released on 2003-01-01 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical continuation methods have provided important contributions toward the numerical solution of nonlinear systems of equations for many years. The methods may be used not only to compute solutions, which might otherwise be hard to obtain, but also to gain insight into qualitative properties of the solutions. Introduction to Numerical Continuation Methods, originally published in 1979, was the first book to provide easy access to the numerical aspects of predictor corrector continuation and piecewise linear continuation methods. Not only do these seemingly distinct methods share many common features and general principles, they can be numerically implemented in similar ways. Introduction to Numerical Continuation Methods also features the piecewise linear approximation of implicitly defined surfaces, the algorithms of which are frequently used in computer graphics, mesh generation, and the evaluation of surface integrals.
Book Synopsis Partial Differential Equations and Functional Analysis by : J. Cea
Download or read book Partial Differential Equations and Functional Analysis written by J. Cea and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pierre Grisvard, one of the most distinguished French mathematicians, died on April 22, 1994. A Conference was held in November 1994 out of which grew the invited articles contained in this volume. All of the papers are related to functional analysis applied to partial differential equations, which was Grisvard's specialty. Indeed his knowledge of this area was extremely broad. He began his career as one of the very first students of Jacques Louis Lions, and in 1965, he presented his "State Thesis" on interpolation spaces, using in particular, spectral theory for linear operators in Banach spaces. After 1970, he became a specialist in the study of optimal regularity for par tial differential equations with boundary conditions. He studied singulari ties coming from coefficients, boundary conditions, and mainly non-smooth domains, and left a legacy of precise results which have been published in journals and books. Pierre Grisvard spent most of his career as a full professor at the University of Nice, where he started in 1967. For shorter or longer periods, he visited several foreign countries, and collaborated with some of the most famous mathematicians in his field. He was also an excellent organizer and directed a large number of Ph.D. students. Finally, this volume contains a bibliography of Grisvard's works as well as one paper which he wrote and which has not been published before.
Book Synopsis Quantitative Stochastic Homogenization and Large-Scale Regularity by : Scott Armstrong
Download or read book Quantitative Stochastic Homogenization and Large-Scale Regularity written by Scott Armstrong and published by Springer. This book was released on 2019-05-09 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: The focus of this book is the large-scale statistical behavior of solutions of divergence-form elliptic equations with random coefficients, which is closely related to the long-time asymptotics of reversible diffusions in random media and other basic models of statistical physics. Of particular interest is the quantification of the rate at which solutions converge to those of the limiting, homogenized equation in the regime of large scale separation, and the description of their fluctuations around this limit. This self-contained presentation gives a complete account of the essential ideas and fundamental results of this new theory of quantitative stochastic homogenization, including the latest research on the topic, and is supplemented with many new results. The book serves as an introduction to the subject for advanced graduate students and researchers working in partial differential equations, statistical physics, probability and related fields, as well as a comprehensive reference for experts in homogenization. Being the first text concerned primarily with stochastic (as opposed to periodic) homogenization and which focuses on quantitative results, its perspective and approach are entirely different from other books in the literature.
Book Synopsis Seminar On Minimal Submanifolds. (AM-103), Volume 103 by : Enrico Bombieri
Download or read book Seminar On Minimal Submanifolds. (AM-103), Volume 103 written by Enrico Bombieri and published by Princeton University Press. This book was released on 2016-03-02 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: The description for this book, Seminar On Minimal Submanifolds. (AM-103), Volume 103, will be forthcoming.
Book Synopsis A New Kind of Science by : Stephen Wolfram
Download or read book A New Kind of Science written by Stephen Wolfram and published by . This book was released on 2002 with total page 1197 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work presents a series of dramatic discoveries never before made public. Starting from a collection of simple computer experiments---illustrated in the book by striking computer graphics---Wolfram shows how their unexpected results force a whole new way of looking at the operation of our universe. Wolfram uses his approach to tackle a remarkable array of fundamental problems in science: from the origin of the Second Law of thermodynamics, to the development of complexity in biology, the computational limitations of mathematics, the possibility of a truly fundamental theory of physics, and the interplay between free will and determinism.
