Anisotropic Sobolev spaces with weights

Abstract

We study Sobolev spaces with weights in the half-space ${\mathbb{R}}_{+}^{N+1}=\{(x,y):x\in {\mathbb{R}}^N,y>0\}$, adapted to the singular elliptic operators \begin{equation*} \mathcal L =y^{α_1}Δ_{x} +y^{α_2}\left(D_{yy}+\frac{c}{y}D_y -\frac{b}{y^2}\right). \end{equation*}