# What is a differentiable functional?

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 $$J(v):= \int_{\Omega}(|\nabla v|^{2} + \chi(\{v>0\})Q^2)$$ is not differentiable. What is a differentiable functional?

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