Potential theory

Author: Zhang Mingyong
Publisher:
Publish Date: 2000-07-01
Features: Since the 20th century, modern potential theory has been formed on the basis of measure theory and topology. This book systematically and incisively presents the fundamental principles and methods of potential theory, summarizing the achievements of modern potential theory research in China since the 1950s, including a significant number of the author's own research findings. The book is divided into five chapters, covering topics such as measure, integration, topology, potentials and harmonic functions, sweeping methods, capacity, the fatness and thinness of point sets and fine topology, Dirichlet problems, and extensions of sweeping methods, among others. Each section is accompanied by a selection of exercises for readers to choose from. The appendix provides a concise introduction to the developments of modern potential theory in various aspects. The book is rigorous in its exposition, easy to understand, thought-provoking, and emphasizes the connections between modern potential theory and physics, differential equations, probability theory, and function theory. It highlights the evolution, development, and influence of potential theory on various disciplines, outlining the research landscape of modern potential theory to pique readers' interest and encourage reflection, guiding them into the field of modern potential theory research. This book can serve as a textbook or reference for senior undergraduate and graduate students in mathematics, applied mathematics, probability, physics, and related fields, as well as for scientific and technological workers engaged in potential theory research and related disciplines.