Dynamical And Geometric Aspects Of Hamilton Jacobi And Linearized Monge Ampere Equations

Author : Hiroyoshi Mitake
Publisher : Springer
ISBN 13 : 3319542087
Total Pages : 233 pages
Book Rating : 4.89/5 ( download)

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Download or read book Dynamical and Geometric Aspects of Hamilton-Jacobi and Linearized Monge-Ampère Equations written by Hiroyoshi Mitake and published by Springer. This book was released on 2017-06-14 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: Consisting of two parts, the first part of this volume is an essentially self-contained exposition of the geometric aspects of local and global regularity theory for the Monge–Ampère and linearized Monge–Ampère equations. As an application, we solve the second boundary value problem of the prescribed affine mean curvature equation, which can be viewed as a coupling of the latter two equations. Of interest in its own right, the linearized Monge–Ampère equation also has deep connections and applications in analysis, fluid mechanics and geometry, including the semi-geostrophic equations in atmospheric flows, the affine maximal surface equation in affine geometry and the problem of finding Kahler metrics of constant scalar curvature in complex geometry. Among other topics, the second part provides a thorough exposition of the large time behavior and discounted approximation of Hamilton–Jacobi equations, which have received much attention in the last two decades, and a new approach to the subject, the nonlinear adjoint method, is introduced. The appendix offers a short introduction to the theory of viscosity solutions of first-order Hamilton–Jacobi equations.

Author : Nam Q. Le
Publisher : American Mathematical Society
ISBN 13 : 1470474204
Total Pages : 599 pages
Book Rating : 4.01/5 ( download)

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Download or read book Analysis of Monge–Ampère Equations written by Nam Q. Le and published by American Mathematical Society. This book was released on 2024-03-07 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic analysis of the Monge–Ampère equation, the linearized Monge–Ampère equation, and their applications, with emphasis on both interior and boundary theories. Starting from scratch, it gives an extensive survey of fundamental results, essential techniques, and intriguing phenomena in the solvability, geometry, and regularity of Monge–Ampère equations. It describes in depth diverse applications arising in geometry, fluid mechanics, meteorology, economics, and the calculus of variations. The modern treatment of boundary behaviors of solutions to Monge–Ampère equations, a very important topic of the theory, is thoroughly discussed. The book synthesizes many important recent advances, including Savin's boundary localization theorem, spectral theory, and interior and boundary regularity in Sobolev and Hölder spaces with optimal assumptions. It highlights geometric aspects of the theory and connections with adjacent research areas. This self-contained book provides the necessary background and techniques in convex geometry, real analysis, and partial differential equations, presents detailed proofs of all theorems, explains subtle constructions, and includes well over a hundred exercises. It can serve as an accessible text for graduate students as well as researchers interested in this subject.

Author : Yves Achdou
Publisher : Springer
ISBN 13 : 3642364330
Total Pages : 316 pages
Book Rating : 4.34/5 ( download)

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Download or read book Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications written by Yves Achdou and published by Springer. This book was released on 2013-05-24 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: These Lecture Notes contain the material relative to the courses given at the CIME summer school held in Cetraro, Italy from August 29 to September 3, 2011. The topic was "Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications". The courses dealt mostly with the following subjects: first order and second order Hamilton-Jacobi-Bellman equations, properties of viscosity solutions, asymptotic behaviors, mean field games, approximation and numerical methods, idempotent analysis. The content of the courses ranged from an introduction to viscosity solutions to quite advanced topics, at the cutting edge of research in the field. We believe that they opened perspectives on new and delicate issues. These lecture notes contain four contributions by Yves Achdou (Finite Difference Methods for Mean Field Games), Guy Barles (An Introduction to the Theory of Viscosity Solutions for First-order Hamilton-Jacobi Equations and Applications), Hitoshi Ishii (A Short Introduction to Viscosity Solutions and the Large Time Behavior of Solutions of Hamilton-Jacobi Equations) and Grigory Litvinov (Idempotent/Tropical Analysis, the Hamilton-Jacobi and Bellman Equations).

Author : Cristian E. Gutierrez
Publisher : Springer Science & Business Media
ISBN 13 : 1461201950
Total Pages : 140 pages
Book Rating : 4.53/5 ( download)

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Download or read book The Monge—Ampère Equation written by Cristian E. Gutierrez and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Piermarco Cannarsa
Publisher : Springer Science & Business Media
ISBN 13 : 0817643362
Total Pages : 311 pages
Book Rating : 4.62/5 ( download)

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Download or read book Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control written by Piermarco Cannarsa and published by Springer Science & Business Media. This book was released on 2004-09-14 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: * A comprehensive and systematic exposition of the properties of semiconcave functions and their various applications, particularly to optimal control problems, by leading experts in the field * A central role in the present work is reserved for the study of singularities * Graduate students and researchers in optimal control, the calculus of variations, and PDEs will find this book useful as a reference work on modern dynamic programming for nonlinear control systems

Author : Andrei D. Polyanin
Publisher : CRC Press
ISBN 13 : 1420010514
Total Pages : 1542 pages
Book Rating : 4.10/5 ( download)

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Download or read book Handbook of Mathematics for Engineers and Scientists written by Andrei D. Polyanin and published by CRC Press. This book was released on 2006-11-27 with total page 1542 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering the main fields of mathematics, this handbook focuses on the methods used for obtaining solutions of various classes of mathematical equations that underlie the mathematical modeling of numerous phenomena and processes in science and technology. The authors describe formulas, methods, equations, and solutions that are frequently used in scientific and engineering applications and present classical as well as newer solution methods for various mathematical equations. The book supplies numerous examples, graphs, figures, and diagrams and contains many results in tabular form, including finite sums and series and exact solutions of differential, integral, and functional equations.

Author : Giorgio Patrizio
Publisher : Springer
ISBN 13 : 3642364217
Total Pages : 328 pages
Book Rating : 4.11/5 ( download)

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Download or read book Pluripotential Theory written by Giorgio Patrizio and published by Springer. This book was released on 2013-05-16 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pluripotential theory is a very powerful tool in geometry, complex analysis and dynamics. This volume brings together the lectures held at the 2011 CIME session on "pluripotential theory" in Cetraro, Italy. This CIME course focused on complex Monge-Ampére equations, applications of pluripotential theory to Kahler geometry and algebraic geometry and to holomorphic dynamics. The contributions provide an extensive description of the theory and its very recent developments, starting from basic introductory materials and concluding with open questions in current research.

Author : Vincent Guedj
Publisher : Springer Science & Business Media
ISBN 13 : 3642236685
Total Pages : 315 pages
Book Rating : 4.86/5 ( download)

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Download or read book Complex Monge–Ampère Equations and Geodesics in the Space of Kähler Metrics written by Vincent Guedj and published by Springer Science & Business Media. This book was released on 2012-01-06 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of these lecture notes is to provide an introduction to the theory of complex Monge–Ampère operators (definition, regularity issues, geometric properties of solutions, approximation) on compact Kähler manifolds (with or without boundary). These operators are of central use in several fundamental problems of complex differential geometry (Kähler–Einstein equation, uniqueness of constant scalar curvature metrics), complex analysis and dynamics. The topics covered include, the Dirichlet problem (after Bedford–Taylor), Monge–Ampère foliations and laminated currents, polynomial hulls and Perron envelopes with no analytic structure, a self-contained presentation of Krylov regularity results, a modernized proof of the Calabi–Yau theorem (after Yau and Kolodziej), an introduction to infinite dimensional riemannian geometry, geometric structures on spaces of Kähler metrics (after Mabuchi, Semmes and Donaldson), generalizations of the regularity theory of Caffarelli–Kohn–Nirenberg–Spruck (after Guan, Chen and Blocki) and Bergman approximation of geodesics (after Phong–Sturm and Berndtsson). Each chapter can be read independently and is based on a series of lectures by R. Berman, Z. Blocki, S. Boucksom, F. Delarue, R. Dujardin, B. Kolev and A. Zeriahi, delivered to non-experts. The book is thus addressed to any mathematician with some interest in one of the following fields, complex differential geometry, complex analysis, complex dynamics, fully non-linear PDE's and stochastic analysis.

Author : Emmanuel Trélat
Publisher : Elsevier
ISBN 13 : 0323858260
Total Pages : 662 pages
Book Rating : 4.67/5 ( download)

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Download or read book Numerical Control: Part B written by Emmanuel Trélat and published by Elsevier. This book was released on 2023-02-20 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Control: Part B, Volume 24 in the Handbook of Numerical Analysis series, highlights new advances in the field, with this new volume presenting interesting chapters written by an international board of authors. Chapters in this volume include Control problems in the coefficients and the domain for linear elliptic equations, Computational approaches for extremal geometric eigenvalue problems, Non-overlapping domain decomposition in space and time for PDE-constrained optimal control problems on networks, Feedback Control of Time-dependent Nonlinear PDEs with Applications in Fluid Dynamics, Stabilization of the Navier-Stokes equations - Theoretical and numerical aspects, Reconstruction algorithms based on Carleman estimates, and more. Other sections cover Discrete time formulations as time discretization strategies in data assimilation, Back and forth iterations/Time reversal methods, Unbalanced Optimal Transport: from Theory to Numerics, An ADMM Approach to the Exact and Approximate Controllability of Parabolic Equations, Nonlocal balance laws -- an overview over recent results, Numerics and control of conservation laws, Numerical approaches for simulation and control of superconducting quantum circuits, and much more. Provides the authority and expertise of leading contributors from an international board of authors Presents the latest release in the Handbook of Numerical Analysis series Updated release includes the latest information on Numerical Control

Author : Jack K. Hale
Publisher : Springer
ISBN 13 :
Total Pages : 536 pages
Book Rating : 4.34/5 ( download)

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Download or read book Dynamics of Infinite Dimensional Systems written by Jack K. Hale and published by Springer. This book was released on 1987-10-29 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the NATO Avanced Study Institute on Dynamics of Infinite Dimensional Systems, held in Lisbon, Portugal, May 19-24, 1986