Nonlinear potential theory

Summary

Nonlinear potential theory extends potential theory from the Laplace equation to nonlinear equations, above all the p-Laplace equation. Its objects are p-harmonic functions, $p$-superharmonic functions, $p$-capacities and nonlinear potentials such as the Wolff potential. Without linearity there is no superposition, so the tools are variational methods, comparison principles and estimates instead of Green's functions. Many classical results survive, including a Wiener criterion for regular boundary points.