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Author: Shuhong Chen
Publisher: LAP Lambert Academic Publishing
ISBN: 9783659278068
Category : Analytic functions
Languages : en
Pages : 296
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Book Description
Regularity theory is one of the most challenging problems in modern theory of partial differential equations. It has attracted peoples' eyes for a long history. A classical method of partial regularity theory is the "freezing the coefficients" method. The proof is complex and troublesome. And the result obtained by this method is not optimal. In this book, we use the method of A-harmonic approximation, to consider regularity theory for nonlinear partial differential systems. The new method not only allows one to simplify the procedure of proof, but also to establish optimal regularity results directly. This book should be useful to professionals in partial differential equations.
Author: Shuhong Chen
Publisher: LAP Lambert Academic Publishing
ISBN: 9783659278068
Category : Analytic functions
Languages : en
Pages : 296
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Book Description
Regularity theory is one of the most challenging problems in modern theory of partial differential equations. It has attracted peoples' eyes for a long history. A classical method of partial regularity theory is the "freezing the coefficients" method. The proof is complex and troublesome. And the result obtained by this method is not optimal. In this book, we use the method of A-harmonic approximation, to consider regularity theory for nonlinear partial differential systems. The new method not only allows one to simplify the procedure of proof, but also to establish optimal regularity results directly. This book should be useful to professionals in partial differential equations.
Author: Alain Bensoussan
Publisher: Springer Science & Business Media
ISBN: 3662129051
Category : Mathematics
Languages : en
Pages : 450
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Book Description
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.
Author: Klaus Ecker
Publisher: Springer Science & Business Media
ISBN: 9780817632434
Category : Mathematics
Languages : en
Pages : 192
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Book Description
* 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.
Author: Alexander D. Ioffe
Publisher: Springer
ISBN: 3319642774
Category : Mathematics
Languages : en
Pages : 509
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Book Description
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.
Author: University of Minnesota. Institute for Mathematics and Its Applications
Publisher:
ISBN:
Category :
Languages : en
Pages : 33
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Book Description
Author: Edgard A. Pimentel
Publisher: Cambridge University Press
ISBN: 1009096664
Category : Mathematics
Languages : en
Pages : 203
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Book Description
A modern account of elliptic regularity theory, with a rigorous presentation of recent developments for fundamental models.
Author: Diogo A. Gomes
Publisher: Springer
ISBN: 3319389343
Category : Mathematics
Languages : en
Pages : 165
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Book Description
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.
Author: Helen Beebee
Publisher: OUP Oxford
ISBN: 0191629464
Category : Philosophy
Languages : en
Pages : 816
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Book Description
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.
Author: Klaus Ecker
Publisher:
ISBN: 9783764332433
Category : Courbure
Languages : en
Pages : 165
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Book Description
This work is 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. A major example is Hamilton's Ricci flow program, which has the aim of settling Thurston's geometrization conjecture, with recent major progress due to Perelman. Another important application of a curvature flow process is the resolution of the famous Penrose conjecture in general relativity by Huisken and Ilmanen. Under mean curvature flow, surfaces usually develop singularities in finite time. This work presents techniques for the study of singularities of mean curvature flow and is largely based on the work of K. Brakke, although more recent developments are incorporated.
Author: University of Minnesota. Institute for Mathematics and Its Applications
Publisher:
ISBN:
Category :
Languages : en
Pages : 11
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Book Description
