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  "body": "\n## Summary\n\nPotential theory is the study of [[harmonic functions|0DEB0JMN0W]], [[subharmonic functions|Z1MHMGFNFW]] and the potentials generated by distributions of mass or charge.\nIt began with the gravitational and electrostatic potentials of physics, which satisfy the Laplace equation away from the masses.\nIts main topics include the [[Dirichlet problem|8D56GQ4AG8]], [[Green's functions|M36SD56MWQ]], [[capacity|DBQXRTC0VN]], [[harmonic measure|CFD7BPM51W]] and the boundary behaviour of harmonic functions.\nIn the plane it is tied closely to complex analysis, since the real part of a [[holomorphic function|0NAHXR1FRH]] is harmonic and $\\log\\abs{f}$ is subharmonic.\n\n## Explanations\n\n### L1 human\n\nThe gravitational pull of a planet or the electric field of a charge can be described by a single number at each point, the potential.\nAway from the masses and charges, this potential satisfies the Laplace equation, so it is a harmonic function.\nPotential theory studies such functions: how they are determined by boundary values, how they behave near the edge of a region, and how charges spread out to minimize energy.\nFor example, the equilibrium temperature in a plate with fixed edge temperatures is a harmonic function, and finding it is a central problem of the theory.\n",
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