##  [Wiener Criterion](/wiener-criterion) 

  ##  [Wiener Criterion](https://puremath.quantumdictionary.io/wiener-criterion-0) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A potential-theoretic condition that characterizes when a boundary point of a domain is regular for the Dirichlet problem for the Laplace operator (or certain linear uniformly elliptic operators): roughly, the point is regular precisely when a capacity-based series or integral computed on complements of shrinking neighborhoods diverges (or converges, depending on normalization).