Lojasiewicz-Simon Gradient Inequalities for Coupled Yang-Mills Energy Functionals

The authors aim to prove Lojasiewicz-Simon gradient inequalities for coupled Yang-Mills energy functions using Sobolev spaces with minimal regularity requirements on connections and sections.

Format: Paperback / softback
Length: 267 pages
Publication date: 01 July 2021
Publisher: American Mathematical Society

The authors primary objective in this monograph is to establish Lojasiewicz-Simon gradient inequalities for coupled Yang-Mills energy functions utilizing Sobolev spaces, which impose minimal regularity conditions on pairs of connections and sections.

The authors begin by introducing the necessary definitions and notations, including the Sobolev space, the gradient operator, and the energy function. They then proceed to derive the gradient inequalities for coupled Yang-Mills energy functions using Sobolev spaces.

The main focus of the monograph is on proving the Lojasiewicz-Simon gradient inequalities for coupled Yang-Mills energy functions. The authors employ various techniques, such as the maximum principle, the Lax-Milgram theorem, and the Sobolev embedding theorem, to achieve this goal.

Throughout the monograph, the authors provide detailed explanations and examples to illustrate the theoretical developments. They also discuss the applications of the gradient inequalities to various physical problems, including the study of black holes and the theory of quantum gravity.

In conclusion, this monograph is a valuable contribution to the field of mathematical physics. It provides a comprehensive treatment of Lojasiewicz-Simon gradient inequalities for coupled Yang-Mills energy functions using Sobolev spaces. The authors' approach is rigorous and well-developed, and the results obtained are of significant importance for understanding the behavior of quantum systems.

Weight: 290g
ISBN-13: 9781470443023