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Titlebook: Classical Potential Theory; David H. Armitage,Stephen J. Gardiner Book 2001 Springer-Verlag London 2001 Analysis.Complex Analysis.Harmonic

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发表于 2025-3-21 18:55:36 | 显示全部楼层 |阅读模式
书目名称Classical Potential Theory
编辑David H. Armitage,Stephen J. Gardiner
视频videohttp://file.papertrans.cn/228/227121/227121.mp4
概述Written by the world leaders in potential theory.Competitive titles are now out of print: an updated introductory text has been long awaited
丛书名称Springer Monographs in Mathematics
图书封面Titlebook: Classical Potential Theory;  David H. Armitage,Stephen J. Gardiner Book 2001 Springer-Verlag London 2001 Analysis.Complex Analysis.Harmonic
描述From its origins in Newtonian physics, potential theory has developed into a major field of mathematical research. This book provides a comprehensive treatment of classical potential theory: it covers harmonic and subharmonic functions, maximum principles, polynomial expansions, Green functions, potentials and capacity, the Dirichlet problem and boundary integral representations. The first six chapters deal concretely with the basic theory, and include exercises. The final three chapters are more advanced and treat topological ideas specifically created for potential theory, such as the fine topology, the Martin boundary and minimal thinness..The presentation is largely self-contained and is accessible to graduate students, the only prerequisites being a reasonable grounding in analysis and several variables calculus, and a first course in measure theory. The book will prove an essential reference to all those with an interest in potential theory and its applications.
出版日期Book 2001
关键词Analysis; Complex Analysis; Harmonic Functions; Poisson integral; Potential theory; Real Analysis; calculu
版次1
doihttps://doi.org/10.1007/978-1-4471-0233-5
isbn_softcover978-1-4471-1116-0
isbn_ebook978-1-4471-0233-5Series ISSN 1439-7382 Series E-ISSN 2196-9922
issn_series 1439-7382
copyrightSpringer-Verlag London 2001
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发表于 2025-3-21 22:47:34 | 显示全部楼层
Book 2001treatment of classical potential theory: it covers harmonic and subharmonic functions, maximum principles, polynomial expansions, Green functions, potentials and capacity, the Dirichlet problem and boundary integral representations. The first six chapters deal concretely with the basic theory, and i
发表于 2025-3-22 00:54:13 | 显示全部楼层
Translators and Publishers: Friends or Foes?ndamental examples as . and .. Also, semicontinuity (rather th an continuity) is the appropriate condition for certain key results (for example, Theorems 3.1.4 and 3.3.1) to hold. The reason for the name “subharmonic” will become apparent in Section 3.2.
发表于 2025-3-22 08:08:37 | 显示全部楼层
1439-7382 From its origins in Newtonian physics, potential theory has developed into a major field of mathematical research. This book provides a comprehensive treatment of classical potential theory: it covers harmonic and subharmonic functions, maximum principles, polynomial expansions, Green functions, pot
发表于 2025-3-22 09:00:31 | 显示全部楼层
Artifacts: The Early Plays Reconsidered,the solution if it exists. For example, if Ω is either a ball or a half-space and . ∈ .(δ.Ω), then the solution of the Dirichlet problem certainly exists and is given by the Poisson integral of .. This follows immediately from Theorems 1.3.3 and 1.7.5. On the other hand, there are quite simple examples in which there is no such solution.
发表于 2025-3-22 14:58:39 | 显示全部楼层
The Dirichlet Problem,the solution if it exists. For example, if Ω is either a ball or a half-space and . ∈ .(δ.Ω), then the solution of the Dirichlet problem certainly exists and is given by the Poisson integral of .. This follows immediately from Theorems 1.3.3 and 1.7.5. On the other hand, there are quite simple examples in which there is no such solution.
发表于 2025-3-22 17:23:11 | 显示全部楼层
Teresa Seruya,José Miranda Justomation. These results will be applied firstly to establish the existence of harmonic functions with prescribed singular parts at a sequence of isolated singularities, and secondly to construct harmonic functions on ℝ . with unexpected properties.
发表于 2025-3-22 21:46:58 | 显示全部楼层
发表于 2025-3-23 05:11:48 | 显示全部楼层
Harmonic Polynomials,mation. These results will be applied firstly to establish the existence of harmonic functions with prescribed singular parts at a sequence of isolated singularities, and secondly to construct harmonic functions on ℝ . with unexpected properties.
发表于 2025-3-23 05:58:10 | 显示全部楼层
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