Lexicographical order: Difference between revisions

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{{unreferenced|date=August 2009}}
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In [[mathematics]], a function <math>f</math> is '''weakly harmonic''' in a domain <math>D</math> if 
:<math>\int_D f\, \Delta g = 0</math>  
 
for all <math>g</math> with [[compact support]] in <math>D</math> and continuous second derivatives, where &Delta; is the [[Laplacian]]. This is the same notion as a [[weak derivative]], however, a function can have a weak derivative and not be differentiable.  In this case, we have the somewhat surprising result that a function is weakly harmonic if and only if it is harmonic.  Thus weakly harmonic is actually equivalent to the seemingly stronger harmonic condition.
 
==See also==
* [[Weak solution]]
* [[Weyl's lemma (Laplace equation)|Weyl's lemma]]
 
{{mathanalysis-stub}}
 
[[Category:Harmonic functions]]

Latest revision as of 03:01, 29 October 2014

My name: Kazuko Tew
My age: 28
Country: France
Home town: Beziers
ZIP: 34500
Address: 26 Rue Marie De Medicis

Also visit my web page :: GHD Hair Straightener

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