##  [Elliptic Regularity](/elliptic-regularity) 

  ##  [Elliptic Regularity](https://natural.quantumdictionary.io/elliptic-regularity-0) 

  

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**Natural & Formal Sciences Dictionary**

 







 

 

 

 



 

 

 

 

Definition

Elliptic regularity is the collection of results that weak solutions of elliptic partial differential equations are in fact smoother than a priori assumed: if L is an elliptic differential operator with sufficiently regular coefficients and L u = f with f smooth (or in suitable Sobolev space), then u inherits additional derivatives up to the regularity allowed by coefficients and boundary.