Potential theory

Summary

Potential theory is the study of harmonic functions, subharmonic functions and the potentials generated by distributions of mass or charge. It began with the gravitational and electrostatic potentials of physics, which satisfy the Laplace equation away from the masses. Its main topics include the Dirichlet problem, Green's functions, capacity, harmonic measure and the boundary behaviour of harmonic functions. In the plane it is tied closely to complex analysis, since the real part of a holomorphic function is harmonic and $\log\abs{f}$ is subharmonic.