Can someone share what usual strategies they pursue for proving Lipschitz? I usually use two strategies but they are very restrictive on the type of functions they require. One is by checking the bound of the continuous derivative, the other is by use of the mean value theorem. Unfortunately the mean value theorem cannot be used in Rn.
Also, the function I'm working is of the type: $\int_0^t f(x(s),y(s))ds$
I am looking for Lipschitz in both $(x(s),y(s))$ with the integrand being bounded by a function of $s$. Lipschitz here does not need to be a constant but may be a function of $t$.
Thanks in advance