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?
What is a differentiable functional?
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functional-analysis
definition
calculus-of-variations
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0@EricStucky: I don't think there is a clear community consensus on this point. See for example [this meta thread](http://meta.math.stackexchange.com/questions/24/answers-that-simply-link-to-a-paper-with-little-or-no-content-in-the-answer-its) where upvoted answers suggested that a link could be an adequate answer. In this case I happen to agree; the question wants a definition, and the answer tells where to find it. Copying the definition would be redundant. If we want to discuss this further it should go to meta. – 2012-08-11