Perron's method: Difference between revisions
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Revision as of 16:12, 8 July 2011
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.[1] 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, taking the Perron solution to be the largest viscosity subsolution, or the least viscosity supersolution.
References
- ↑ Perron, O. (12 1923), "Eine neue Behandlung der ersten Randwertaufgabe für Δu=0", Mathematische Zeitschrift (Springer Berlin / Heidelberg) 18 (1): 42–54, doi:10.1007/BF01192395, ISSN 0025-5874