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Can anyone think of an example $u\in L^2(\mathbb{R}^2)$ such that $u$ is smooth in $x_1$ but nowhere differentiable in $x_2$?

Karo
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    What about (the direct product of a constant function and the Weierstrass nowhere differentiable function) x a bump function? – Elle Najt Feb 11 '14 at 05:00

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