The title of this question is quite self-explanatory, I was wondering if it's possible to find a function $g(x,u)=f(ue^{x^2})$ is a (uniformly) Lipschitz continuous function both in $u\in\mathbb R$ and $x\in\mathbb R$.
2026-04-02 02:55:43.1775098543
Is it possible to find a function $f$ such that $f(ue^{x^2})$ is uniformly Lipschitz in $u$ and $x$?
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