SCHWEITZER 2020 Problem 11

Given a real number $p>1$ , a continuous function $h\colon [0,\infty)\to [0,\infty)$ , and a smooth vector field $Y\colon \mathbb{R}^n \to \mathbb{R}^n$ with $\mathrm{div}~Y=0$ , prove the following inequality $$\int_{\mathbb{R}^n}h(|x|)|x|^{p}\leq \int_{\mathbb{R}^{n}}h(|x|)|x+Y(x)|^{p}.$$