Equation 3.1.9EB7C9EF52470

\begin{equation} \begin{split} u_\varepsilon (x)& =\int _{B(0,\varepsilon )}u(x+y)\rho _\varepsilon (y)\, \mathrm dy=s_{d-1}\int _0^\varepsilon r^{d-1}\phi _\varepsilon (r)M_ u(x,r)\, \mathrm dr\\ & =u(x)\, s_{d-1}\int _0^\varepsilon r^{d-1}\phi _\varepsilon (r)\, \mathrm dr=u(x)\int _{\mathbb R^ d}\rho _\varepsilon \, \mathrm dy=u(x). \end{split} \end{equation}