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I saw in the article Alt, H. M. and Caffarelli, L. A. Existence and regularity for a minimum problem with free boundary. J. Reine Angew. Math., 325, (1981), 105–144. That the functional \begin{equation} J(v):= \int_{\Omega}(|\nabla v|^{2} + \chi(\{v>0\})Q^2) \end{equation} is not differentiable. What is a differentiable functional?

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http://en.wikipedia.org/wiki/Fr%C3%A9chet_derivative

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Can you flesh out the answer so that it includes more than just a link to Wikipedia? –  Chris Taylor Aug 11 '12 at 1:41
    
The definition of a differentiable functional can be found on the link I just gave –  Mercy Aug 11 '12 at 3:15
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Mercy, anyone who does not or cannot click this link cannot benefit from this answer. If this link ever fails, this answer is worthless. If a person is living in a country that censors Wikipedia, this answer is worthless. If the page is vandalized, this answer is difficult. If a person has poor internet connection, this answer is difficult. This site is intended to serve many needs, including those of the question asker, currently interested parties, and future learners. Thus a post whose sole mathematical content is a link is generally considered not in line with the goals of the site. –  Eric Stucky Aug 11 '12 at 3:43
    
@EricStucky You could have given a short answer instead of making the long comment! –  Mercy Aug 11 '12 at 7:41
    
@Mercy: He could, but usually it pays off to explain to people why a change is necessary instead of just doing it. –  blubb Aug 11 '12 at 9:56
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