Homogenization of diffusion processes with singular drifts and potentials via unfolding method

This work is concerned with homogenization problems for elliptic equations of the type $$\{\begin{array}{l}{\mathfrak{L}}_{\delta }{u}_{\delta }+\lambda u_{\delta }=f_{\delta }\text{in}D,\\ u=0\text{on}\mathrm{\partial }D,\end{array}$$ where $\delta >0$, $\lambda \in \mathbb{R}$, $D$ is a bounded open set in ${\mathbb{R}}^d$, and $f_{\delta }\in H^{-1}(D)$. The operator ${\mathfrak{L}}_{\delta }u=-\mathrm{d}\mathrm{i}\mathrm{v}(A^{\delta }\mathrm{\nabla }u+C^{\delta }u)+B^{\delta }\mathrm{\nabla }u+k^{\delta }u$ involved uniformly bounded diffusion coefficients $A^{\delta }$, where drifts $B^{\delta }$, $C^{\delta }$, and potential $k^{\delta }$ are possibly unbounded. An application to homogenization of the corresponding diffusion processes is also discussed.