##  [Barrier Condition](/barrier-condition) 

  ##  [Barrier Condition](https://puremath.quantumdictionary.io/barrier-condition-0) 

  

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**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The requirement that at a given boundary point there exists a positive superharmonic function (a barrier) defined in a neighborhood of the point, vanishing at the point and strictly positive in the punctured neighborhood, which forces Perron envelopes to attain the boundary value and thereby guarantees pointwise solvability.