View source for Perron's method

'''Perron's method''', also known as the '''method of subharmonic functions''', is a technique originally introduced by Oskar Perron for the solution of the Dirichlet problem for Laplace's equation.<ref>{{Citation | last1=Perron | first1=O. |  title=Eine neue Behandlung der ersten Randwertaufgabe für Δu=0 | publisher=Springer Berlin / Heidelberg | doi=10.1007/BF01192395 | year=1923 | month=12 | journal=Mathematische Zeitschrift| issn=0025-5874 | volume=18 | issue=1 | pages=42–54}}
</ref> The Perron method works by finding the largest subharmonic function with boundary values below the desired values; the "Perron solution" coincides with the actual solution of the Dirichlet problem if the problem is soluble. 

The Perron method can be used [[viscosity solutions]] whenever a [[comparison principle]] is available and appropriate barriers can be constructed to assure the boundary conditions. The Perron solution is taken to be the largest viscosity subsolution, or the least viscosity supersolution. 

==References==
{{reflist}}