Suppose I want to show that f(t, y) = e^(t - y) satisfies a Lipschitz condition on D = {(t, y): 0 <= t <= 1, -inf < y < inf}.

I want to show |f(t, y1) - f(t, y2)| <= L |y1 - y2|.

Do I just pick arbitrary values for t, y1, y2, and L? E.g. t = 1, y1 = 1, y2 = 0, so

|1 - e| <= L

and I can just say that this satisfies a Lipschitz condition for L = 2?

Hey do you think that this
$
\int_0^x \delta\left(\sin\pi\left(\frac{n\pm 1}4\right)\right)\pi'(n)dn
$
would work as a prime counting function for primes of the form $4n\pm 1$?

well good nite and good luck with your sciatic nerve, @jonas
and like this waiter once said: beer always helps $\color{green}{.}\!\color{goldenrod}{.}\!\color{red}{.}$