Potential theory

Author: Zhang Mingyong
Editor-in-Chief: Liu Yong et al.
Publisher:
Publish Date: 1998-12-01
Features: This series is intended for senior undergraduate students, graduate students, young teachers, and mathematicians engaged in research in mathematics, computational mathematics, probability and statistics, and related fields. The series features up-to-date content, aiming to reflect the latest achievements in modern mathematics; it is concise in presentation, approximately equivalent to the material covered in a graduate course with 3 weekly hours per semester. The primary purpose of editing and publishing this series is to meet the needs of our country in training graduate students. At the same time, it can serve as a reference book for senior undergraduate elective courses in mathematics and related disciplines, contributing to the improvement of undergraduate teaching quality. We sincerely hope that readers will provide valuable feedback on the selection of titles and the choice of content, which will serve as a reference for future publications or revisions. Editorial Committee of the Mathematics Series of Peking University January 1981
Book Description Since the 20th century, modern potential theory has been developed 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, potential and harmonic functions, sweeping methods, capacity, the fatness and thinness of point sets and fine topology, Dirichlet problems, and extensions of sweeping methods. Each section is accompanied by a sufficient number of exercises for readers to choose from. The appendix provides a concise introduction to the development of modern potential theory in various aspects. The book is rigorous in its presentation, yet accessible and thought-provoking. It emphasizes the connections between modern potential theory and physics, differential equations, probability theory, and function theory, highlighting the evolution, development, and influence of potential theory on various disciplines. It outlines the research landscape of modern potential theory, aiming 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 disciplines. It is also suitable for researchers and professionals engaged in potential theory research and related fields.