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Global Regularity for the Yang-Mills Equations on High Dimensional Minkowski Space

Joachim Krieger University of Pennsylvania, Philadelphia, PA
Jacob Sterbenz University of California, San Diego, La Jolla, CA
Available Formats:
Electronic ISBN: 978-0-8218-9871-0
Product Code: MEMO/223/1047.E
List Price: $69.00 MAA Member Price:$62.10
AMS Member Price: $41.40 Click above image for expanded view Global Regularity for the Yang-Mills Equations on High Dimensional Minkowski Space Joachim Krieger University of Pennsylvania, Philadelphia, PA Jacob Sterbenz University of California, San Diego, La Jolla, CA Available Formats:  Electronic ISBN: 978-0-8218-9871-0 Product Code: MEMO/223/1047.E  List Price:$69.00 MAA Member Price: $62.10 AMS Member Price:$41.40
• Book Details

Memoirs of the American Mathematical Society
Volume: 2232013; 99 pp
MSC: Primary 35; Secondary 70;

This monograph contains a study of the global Cauchy problem for the Yang-Mills equations on $(6+1)$ and higher dimensional Minkowski space, when the initial data sets are small in the critical gauge covariant Sobolev space $\dot{H}_A^{(n-4)/{2}}$. Regularity is obtained through a certain “microlocal geometric renormalization” of the equations which is implemented via a family of approximate null Crönstrom gauge transformations. The argument is then reduced to controlling some degenerate elliptic equations in high index and non-isotropic $L^p$ spaces, and also proving some bilinear estimates in specially constructed square-function spaces.

• Chapters
• 1. Introduction
• 2. Some Gauge-Theoretic Preliminaries
• 3. Reduction to the “Main a-Priori Estimate”
• 4. Some Analytic Preliminaries
• 5. Proof of the Main A-Priori Estimate
• 6. Reduction to Approximate Half-Wave Operators
• 7. Construction of the Half-Wave Operators
• 8. Fixed Time $L^2$ Estimates for the Parametrix
• 9. The Dispersive Estimate
• 10. Decomposable Function Spaces and Some Applications
• 11. Completion of the Proof
• Requests

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Volume: 2232013; 99 pp
MSC: Primary 35; Secondary 70;

This monograph contains a study of the global Cauchy problem for the Yang-Mills equations on $(6+1)$ and higher dimensional Minkowski space, when the initial data sets are small in the critical gauge covariant Sobolev space $\dot{H}_A^{(n-4)/{2}}$. Regularity is obtained through a certain “microlocal geometric renormalization” of the equations which is implemented via a family of approximate null Crönstrom gauge transformations. The argument is then reduced to controlling some degenerate elliptic equations in high index and non-isotropic $L^p$ spaces, and also proving some bilinear estimates in specially constructed square-function spaces.

• Chapters
• 1. Introduction
• 2. Some Gauge-Theoretic Preliminaries
• 3. Reduction to the “Main a-Priori Estimate”
• 4. Some Analytic Preliminaries
• 5. Proof of the Main A-Priori Estimate
• 6. Reduction to Approximate Half-Wave Operators
• 7. Construction of the Half-Wave Operators
• 8. Fixed Time $L^2$ Estimates for the Parametrix
• 9. The Dispersive Estimate
• 10. Decomposable Function Spaces and Some Applications
• 11. Completion of the Proof
Review Copy – for reviewers who would like to review an AMS book
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Accessibility – to request an alternate format of an AMS title
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