Consider the following Hamilton-Jacobi (HJ) equation:
$$u_t + H(\nabla u,x) = 0 \quad \text{ in } \mathbb{R}^n \times (0, T], $$ where $u:\mathbb{R}^n \times (0,T] \to \mathbb{R}$, and $H:\mathbb{R}^n \times \mathbb{R}^n \to \mathbb{R}$ (*Hamiltonian*) is continuous.
Consider the initial condition $$u = g \quad \text{ in } \mathbb{R}^n \times \{t = 0\}.$$

In his textbook on *Partial Differential Equations* (pages 586-590), Evans proves uniqueness of viscosity solutions of this initial value problem under the following assumptions:
$$\vert H(p,x) - H(q,x) \vert \le C \vert p - q \vert;$$
$$\vert H(p,x) - H(p,y)\vert \le C \vert x-y \vert (1+\vert p \vert),$$ for some $C \ge 0.$ Evans' proof is relatively simple to follow, but slightly technical and, at least to me, not quite enlightening.

**Question:** Where can I find an alternative proof of this result?

**Side remark:** In [CEL84], Crandall, Lions, and Evans prove existence and uniqueness of viscosity solutions for a less general Hamiltonian.