Let $f$ be a function that is equal to $x$ for $t<0$ and $y$ for $t\ge0$. Can we write down the weak derivative of this function at $t=0$?
2026-03-28 15:18:48.1774711128
Weak derivative of generalized stepfunction?
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The weak derivative is $(y-x) \delta(t)$, assuming $x,y$ are fixed.