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Hamilton–Jacobi Equations: Theory and Applications

Hung Vinh Tran University of Wisconsin, Madison, WI
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Softcover ISBN: 978-1-4704-6555-1
Product Code: GSM/213.S
List Price: $85.00 MAA Member Price:$76.50
AMS Member Price: $68.00 Electronic ISBN: 978-1-4704-6554-4 Product Code: GSM/213.E List Price:$85.00
MAA Member Price: $76.50 AMS Member Price:$68.00
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List Price: $127.50 MAA Member Price:$114.75
AMS Member Price: $102.00 Click above image for expanded view Hamilton–Jacobi Equations: Theory and Applications Hung Vinh Tran University of Wisconsin, Madison, WI Available Formats:  Softcover ISBN: 978-1-4704-6555-1 Product Code: GSM/213.S  List Price:$85.00 MAA Member Price: $76.50 AMS Member Price:$68.00
 Electronic ISBN: 978-1-4704-6554-4 Product Code: GSM/213.E
 List Price: $85.00 MAA Member Price:$76.50 AMS Member Price: $68.00 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$127.50 MAA Member Price: $114.75 AMS Member Price:$102.00
• Book Details

Volume: 2132021; 322 pp
MSC: Primary 35; Secondary 49; 37;

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 reference. It can also serve as a gentle introductory reference to the homogenization theory.

Graduate students and researchers interested in Hamilton–Jacobi equations and viscosity solutions.

• Chapters
• Introduction to viscosity solutions for Hamilton–Jacobi equations
• First-order Hamilton–Jacobi equations with convex Hamiltonians
• First-order Hamilton–Jacobi equations with possibly nonconvex Hamiltonians
• Periodic homogenization theory for Hamilton–Jacobi equations
• Almost periodic homogenization theory for Hamilton–Jacobi equations
• First-order convex Hamilton–Jacobi equations in a torus
• Introduction to weak KAM theory
• Further properties of the effective Hamiltonians in the convex setting
• Notations
• Sion’s minimax theorem
• Characterization of the Legendre transform
• Existence and regularity of minimizers for action functionals
• Boundary value problems
• Sup-convolutions
• Sketch of proof of Theorem 6.26
• Solutions to some exercises

• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 2132021; 322 pp
MSC: Primary 35; Secondary 49; 37;

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 reference. It can also serve as a gentle introductory reference to the homogenization theory.

Graduate students and researchers interested in Hamilton–Jacobi equations and viscosity solutions.

• Chapters
• Introduction to viscosity solutions for Hamilton–Jacobi equations
• First-order Hamilton–Jacobi equations with convex Hamiltonians
• First-order Hamilton–Jacobi equations with possibly nonconvex Hamiltonians
• Periodic homogenization theory for Hamilton–Jacobi equations
• Almost periodic homogenization theory for Hamilton–Jacobi equations
• First-order convex Hamilton–Jacobi equations in a torus
• Introduction to weak KAM theory
• Further properties of the effective Hamiltonians in the convex setting
• Notations
• Sion’s minimax theorem
• Characterization of the Legendre transform
• Existence and regularity of minimizers for action functionals
• Boundary value problems
• Sup-convolutions
• Sketch of proof of Theorem 6.26
• Solutions to some exercises
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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