Dynamical and Geometric Aspects of Hamilton-Jacobi and Linearized Monge-Ampère Equations

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Publisher : Springer
ISBN 13 : 3319542087
Total Pages : 233 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Dynamical and Geometric Aspects of Hamilton-Jacobi and Linearized Monge-Ampère Equations by : Hiroyoshi Mitake

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.

Analysis of Monge–Ampère Equations

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Publisher : American Mathematical Society
ISBN 13 : 1470474204
Total Pages : 599 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Analysis of Monge–Ampère Equations by : Nam Q. Le

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.

Hamilton–Jacobi Equations: Theory and Applications

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Publisher : American Mathematical Soc.
ISBN 13 : 1470465116
Total Pages : 322 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Hamilton–Jacobi Equations: Theory and Applications by : Hung V. Tran

Download or read book Hamilton–Jacobi Equations: Theory and Applications written by Hung V. Tran and published by American Mathematical Soc.. This book was released on 2021-08-16 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an extensive survey of many important topics in the theory of Hamilton–Jacobi equations with particular emphasis on modern approaches and viewpoints. Firstly, the basic well-posedness theory of viscosity solutions for first-order Hamilton–Jacobi equations is covered. Then, the homogenization theory, a very active research topic since the late 1980s but not covered in any standard textbook, is discussed in depth. Afterwards, dynamical properties of solutions, the Aubry–Mather theory, and weak Kolmogorov–Arnold–Moser (KAM) theory are studied. Both dynamical and PDE approaches are introduced to investigate these theories. Connections between homogenization, dynamical aspects, and the optimal rate of convergence in homogenization theory are given as well. The book is self-contained and is useful for a course or for references. It can also serve as a gentle introductory reference to the homogenization theory.

Hamiltonian Dynamics

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Publisher : World Scientific
ISBN 13 : 9810233086
Total Pages : 457 pages
Book Rating : 4.8/5 (12 download)

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Book Synopsis Hamiltonian Dynamics by : Gaetano Vilasi

Download or read book Hamiltonian Dynamics written by Gaetano Vilasi and published by World Scientific. This book was released on 2001 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is both a textbook and a monograph. It is partially based on a two-semester course, held by the author for third-year students in physics and mathematics at the University of Salerno, on analytical mechanics, differential geometry, symplectic manifolds and integrable systems.As a textbook, it provides a systematic and self-consistent formulation of Hamiltonian dynamics both in a rigorous coordinate language and in the modern language of differential geometry. It also presents powerful mathematical methods of theoretical physics, especially in gauge theories and general relativity.As a monograph, the book deals with the advanced research topic of completely integrable dynamics, with both finitely and infinitely many degrees of freedom, including geometrical structures of solitonic wave equations.

Generalized Solutions of Hamilton-Jacobi Equations

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Author :
Publisher : Pitman Publishing
ISBN 13 :
Total Pages : 332 pages
Book Rating : 4.:/5 (44 download)

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Book Synopsis Generalized Solutions of Hamilton-Jacobi Equations by : Pierre-Louis Lions

Download or read book Generalized Solutions of Hamilton-Jacobi Equations written by Pierre-Louis Lions and published by Pitman Publishing. This book was released on 1982 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a complete and self-contained treatment of Hamilton-Jacobi equations. The author gives a new presentation of classical methods and of the relations between Hamilton-Jacobi equations and other fields. This complete treatment of both classical and recent aspects of the subject is presented in such a way that it requires only elementary notions of analysis and partial differential equations.

Hamilton-Jacobi Equations in Hilbert Spaces

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Publisher : Pitman Advanced Publishing Program
ISBN 13 :
Total Pages : 188 pages
Book Rating : 4.:/5 (44 download)

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Book Synopsis Hamilton-Jacobi Equations in Hilbert Spaces by : Viorel Barbu

Download or read book Hamilton-Jacobi Equations in Hilbert Spaces written by Viorel Barbu and published by Pitman Advanced Publishing Program. This book was released on 1983 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: This presents a self-contained treatment of Hamilton-Jacobi equations in Hilbert spaces. Most of the results presented have been obtained by the authors. The treatment is novel in that it is concerned with infinite dimensional Hamilton-Jacobi equations; it therefore does not overlap with Research Note #69. Indeed, these books are in a sense complementary.

Handbook of Mathematics for Engineers and Scientists

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Publisher : CRC Press
ISBN 13 : 1420010514
Total Pages : 1542 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Handbook of Mathematics for Engineers and Scientists by : Andrei D. Polyanin

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.

Pluripotential Theory

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Publisher : Springer
ISBN 13 : 3642364217
Total Pages : 328 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Pluripotential Theory by : Giorgio Patrizio

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.

Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications

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Publisher : Springer
ISBN 13 : 9783642364327
Total Pages : 0 pages
Book Rating : 4.3/5 (643 download)

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Book Synopsis Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications by : Yves Achdou

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 2013-06-03 with total page 0 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).

The Hamilton-Jacobi Theory in the Calculus of Variations

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Author :
Publisher : Krieger Publishing Company
ISBN 13 :
Total Pages : 422 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis The Hamilton-Jacobi Theory in the Calculus of Variations by : Hanno Rund

Download or read book The Hamilton-Jacobi Theory in the Calculus of Variations written by Hanno Rund and published by Krieger Publishing Company. This book was released on 1966 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Complex Monge–Ampère Equations and Geodesics in the Space of Kähler Metrics

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Publisher : Springer Science & Business Media
ISBN 13 : 3642236685
Total Pages : 315 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Complex Monge–Ampère Equations and Geodesics in the Space of Kähler Metrics by : Vincent Guedj

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.

Numerical Control: Part B

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Publisher : Elsevier
ISBN 13 : 0323858260
Total Pages : 662 pages
Book Rating : 4.3/5 (238 download)

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Book Synopsis Numerical Control: Part B by : Emmanuel Trélat

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

Separation of Variables in the Special Diagonal Hamilton-Jacobi Equation

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Publisher :
ISBN 13 :
Total Pages : 84 pages
Book Rating : 4.:/5 (317 download)

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Book Synopsis Separation of Variables in the Special Diagonal Hamilton-Jacobi Equation by : David L. Blanchard

Download or read book Separation of Variables in the Special Diagonal Hamilton-Jacobi Equation written by David L. Blanchard and published by . This book was released on 1973 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematical Models and Integration Methods

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Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3111546667
Total Pages : 180 pages
Book Rating : 4.1/5 (115 download)

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Book Synopsis Mathematical Models and Integration Methods by : Oleg V. Kaptsov

Download or read book Mathematical Models and Integration Methods written by Oleg V. Kaptsov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2024-09-23 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book compiles works presented at a seminar aiming to attract global experts in differential equations, mathematical modeling, and integration methods. It covers classical and contemporary integration techniques for partial differential equations, including Monge and Darboux's approaches and their extensions. Additionally, it introduces a novel theoretical model for plane turbulent flows, presents gravitational equations derived from the principle of least action, and explores symmetry-preserving conservative finite-difference schemes for hydrodynamic-type equations. Analytical solutions for Maxwell's equations in incompressible viscoelastic mediums are examined, alongside theoretical-group analysis of wake mathematical models and reduction to ordinary differential equations. The book also delves into special classes of two-dimensional ideal fluid motion and advancements in discrete orthogonal polynomial theory, showcasing rapid decay properties near interval boundaries. In conclusion, this comprehensive collection is indispensable for researchers and practitioners in applied mathematics, fluid dynamics, and computational modeling, providing valuable insights into cutting-edge methods and solutions in the field.

Degenerate Complex Monge--Ampère Equations

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Publisher :
ISBN 13 : 9783037196670
Total Pages : pages
Book Rating : 4.1/5 (966 download)

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Book Synopsis Degenerate Complex Monge--Ampère Equations by : VINCENT GUEDJ; AHMED ZERIAHI.

Download or read book Degenerate Complex Monge--Ampère Equations written by VINCENT GUEDJ; AHMED ZERIAHI. and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Winner of the 2016 EMS Monograph Award! Complex Monge-Ampère equations have been one of the most powerful tools in Kähler geometry since Aubin and Yau's classical works, culminating in Yau's solution to the Calabi conjecture. A notable application is the construction of Kähler-Einstein metrics on some compact Kähler manifolds. In recent years degenerate complex Monge-Ampère equations have been intensively studied, requiring more advanced tools. The main goal of this book is to give a self-contained presentation of the recent developments of pluripotential theory on compact Kähler manifolds and its application to Kähler-Einstein metrics on mildly singular varieties. After reviewing basic properties of plurisubharmonic functions, Bedford-Taylor's local theory of complex Monge-Ampère measures is developed. In order to solve degenerate complex Monge-Ampère equations on compact Kähler manifolds, fine properties of quasi-plurisubharmonic functions are explored, classes of finite energies defined and various maximum principles established. After proving Yau's celebrated theorem as well as its recent generalizations, the results are then used to solve the (singular) Calabi conjecture and to construct (singular) Kähler-Einstein metrics on some varieties with mild singularities. The book is accessible to advanced students and researchers of complex analysis and differential geometry.

Scientific and Technical Aerospace Reports

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Publisher :
ISBN 13 :
Total Pages : 1346 pages
Book Rating : 4.:/5 (31 download)

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Book Synopsis Scientific and Technical Aerospace Reports by :

Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1985 with total page 1346 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematical Reviews

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Publisher :
ISBN 13 :
Total Pages : 1770 pages
Book Rating : 4.X/5 (6 download)

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Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 2004 with total page 1770 pages. Available in PDF, EPUB and Kindle. Book excerpt: