Classical Potential Theory

Front Cover
Springer Science & Business Media, 2001 - Mathematics - 333 pages
0 Reviews
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.
  

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

II
1
III
3
IV
6
V
13
VI
15
VII
19
VIII
22
IX
26
XLIII
163
XLIV
164
XLV
167
XLVI
172
XLVII
177
XLVIII
179
XLIX
188
L
189

X
30
XI
33
XII
35
XIII
37
XIV
40
XV
47
XVI
53
XVII
55
XVIII
59
XIX
64
XX
68
XXI
72
XXII
75
XXIII
79
XXIV
82
XXV
84
XXVI
89
XXVII
96
XXVIII
100
XXIX
105
XXX
109
XXXI
112
XXXII
118
XXXIII
123
XXXIV
127
XXXV
129
XXXVI
134
XXXVII
137
XXXVIII
143
XXXIX
146
XL
150
XLI
156
XLII
159
LI
191
LII
192
LIII
193
LIV
197
LV
199
LVI
201
LVII
206
LVIII
208
LIX
214
LX
217
LXI
221
LXII
226
LXIII
233
LXIV
241
LXV
246
LXVI
250
LXVII
252
LXVIII
256
LXIX
259
LXX
269
LXXI
273
LXXII
279
LXXIII
284
LXXIV
287
LXXV
290
LXXVI
294
LXXVII
296
LXXVIII
305
LXXIX
309
LXXX
317
LXXXI
329
LXXXII
331
Copyright

Common terms and phrases

References to this book

All Book Search results »

About the author (2001)

Stephen Gardiner is Associate Professor of Mathematics at University College Dublen.