Global regularity for the Yang-Mills equations on high dimensional Minkowski space
著者
書誌事項
Global regularity for the Yang-Mills equations on high dimensional Minkowski space
（Memoirs of the American Mathematical Society, no. 1047）
American Mathematical Society, c2012
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注記
"May 2013, volume 223, number 1047 (first of 5 numbers)."
Includes bibliographical references (p. 99)
内容説明・目次
内容説明
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 H (n 4)/2A. Regularity is obtained through a certain ""microlocal geometric renormalization"" of the equations which is implemented via a family of approximate null Croenstrom gauge transformations. The argument is then reduced to controlling some degenerate elliptic equations in high index and non-isotropic Lp spaces, and also proving some bilinear estimates in specially constructed square-function spaces.
目次
Table of Contents
Introduction
Some gauge-theoretic preliminaries
Reduction to the ""main a-priori estimate""
Some analytic preliminaries
Proof of the main a-priori estimate
Reduction to approximate half-wave operators
Construction of the half-wave operators
Fixed time L2 estimates for the parametrix
The dispersive estimate
Decomposable function spaces and some applications
Completion of the proof
Bibliography
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