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The Yangmills Heat Equation With Finite Action In Three Dimensions Leonard Gross

  • SKU: BELL-48041730
The Yangmills Heat Equation With Finite Action In Three Dimensions Leonard Gross
$ 31.00 $ 45.00 (-31%)

4.4

72 reviews

The Yangmills Heat Equation With Finite Action In Three Dimensions Leonard Gross instant download after payment.

Publisher: American Mathematical Society
File Extension: PDF
File size: 1.25 MB
Pages: 111
Author: Leonard Gross
ISBN: 9781470450533, 1470450534
Language: English
Year: 2022

Product desciption

The Yangmills Heat Equation With Finite Action In Three Dimensions Leonard Gross by Leonard Gross 9781470450533, 1470450534 instant download after payment.

The existence and uniqueness of solutions to the Yang-Mills heat equation is proven over R 3 and over a bounded open convex set in R 3 . The initial data is taken to lie in the Sobolev space of order one half, which is the critical Sobolev index for this equation over a three dimensional manifold. The existence is proven by solving first an augmented, strictly parabolic equation and then gauge transforming the solution to a solution of the Yang-Mills heat equation itself. The gauge functions needed to carry out this procedure lie in the critical gauge group of Sobolev regularity three halves, which is a complete topological group in a natural metric but is not a Hilbert Lie group. The nature of this group must be understood in order to carry out the reconstruction procedure. Solutions to the Yang-Mills heat equation are shown to be strong solutions modulo these gauge functions. Energy inequalities and Neumann domination inequalities are used to establish needed initial behavior properties of solutions to the augmented equation.

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