Potential theory Dirichlet problem and Green's functions Concept
Perron method
Summary
The Perron method solves the Dirichlet problem for the Laplacian on an arbitrary bounded open set. It takes the upper envelope of all subharmonic functions that lie below the boundary data at the boundary. This envelope is always harmonic; the only question is whether it takes the right boundary values. That question is local and leads to barriers and regular boundary points.
Further reading
About this page
| Tag | AEZ7PPCNQS |
|---|---|
| URI | m2://AEZ7PPCNQS |
| Kind | concept |
| Writing | W0 stub |
| MSC | 31B20, 31A25, 35J25 |
| Same as |
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