##  [Perron Method](/perron-method) 

  ##  [Perron Method](https://puremath.quantumdictionary.io/perron-method-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A technique for constructing a solution of the Dirichlet problem by taking the upper envelope of all subharmonic functions bounded above by the prescribed boundary data (or dually the lower envelope of superharmonic functions); the resulting Perron solution is harmonic in the domain where the envelope is not −∞ and attains boundary values at regular points.