Hey guys I want to clarify something so If someone could help me would be great
For a function $F(U, x, t): \mathbb{R}^2 \times \mathbb{R} \times[0, \infty) \rightarrow \mathbb{R}^2$, the following inequality is proving that $F$ is Lipschitz with respect the variable x
$$
\|V\|_{\infty} \leq M \text { and }\|W\|_{\infty} \leq M \Rightarrow\|F(V, \cdot, t)-F(W, \cdot, t)\|_{\infty} \leq k_3\|V-W\|_{\infty}.
$$
have in mind that $U:\mathbb{R} \times[0, \infty) \rightarrow \mathbb{R}$. Can someone helpe with this please, since the $\cdot$ are confusing me or is the inequality only proving Lip…