Potential Theory [2 ed.] 9780387102764, 0-387-10276-0
236 6 842KB
English Pages 174 [172] Year 1981
Table of contents :
Electrostatics....Pages 1-10
Poisson's equation....Pages 11-16
Fundamental solutions....Pages 17-25
Capacity....Pages 26-33
Energy....Pages 34-40
Existence of the equilibrium distribution....Pages 41-49
Maximum principle for potentials....Pages 50-55
Uniqueness of the equilibrium distribution....Pages 56-59
The cone condition....Pages 60-65
Singularities of bounded harmonic functions....Pages 66-73
Green's function....Pages 74-83
The kelvin transform....Pages 84-90
Perron's method....Pages 91-99
Barriers....Pages 100-107
Kellogg's theorem....Pages 108-113
The riesz decomposition theorem....Pages 114-128
Applications of the riesz decomposition....Pages 129-137
Wiener's criterion....Pages 138-157
Electrostatics....Pages 1-10
Poisson's equation....Pages 11-16
Fundamental solutions....Pages 17-25
Capacity....Pages 26-33
Energy....Pages 34-40
Existence of the equilibrium distribution....Pages 41-49
Maximum principle for potentials....Pages 50-55
Uniqueness of the equilibrium distribution....Pages 56-59
The cone condition....Pages 60-65
Singularities of bounded harmonic functions....Pages 66-73
Green's function....Pages 74-83
The kelvin transform....Pages 84-90
Perron's method....Pages 91-99
Barriers....Pages 100-107
Kellogg's theorem....Pages 108-113
The riesz decomposition theorem....Pages 114-128
Applications of the riesz decomposition....Pages 129-137
Wiener's criterion....Pages 138-157
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