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  "body": "\n## Summary\n\nNonlinear potential theory extends [[potential theory|9PM8Q2E30Q]] from the Laplace equation to nonlinear equations, above all the [[p-Laplace equation|XJMYGY0ZZF]].\nIts objects are [[p-harmonic functions|7BKQT71FYZ]], $p$-superharmonic functions, $p$-capacities and nonlinear potentials such as the [[Wolff potential|EBD8TWFNS0]].\nWithout linearity there is no superposition, so the tools are variational methods, comparison principles and estimates instead of Green's functions.\nMany classical results survive, including a Wiener criterion for regular boundary points.\n\n## Explanations\n\n### L1 human\n\nClassical potential theory studies harmonic functions, which minimize the energy $\\int \\abs{\\nabla u}^2$.\nNonlinear potential theory studies functions that minimize energies such as $\\int \\abs{\\nabla u}^p$ with $p \\ne 2$.\nFor these equations the sum of two solutions is no longer a solution, so a potential cannot be built by adding up the effects of point charges.\nEven so, one can define the size of a set, its capacity, and decide which boundary points are well behaved, much as in the classical case.\nThe Wiener criterion for the $p$-Laplacian was proved sufficient by Maz'ya and necessary by Kilpeläinen and Malý.\n",
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