Potential Theory

John Wermer (auth.)9780387102764, 0-387-10276-0

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