A unified approach to degenerate problems in the half-space

Abstract

We study elliptic and parabolic problems governed by 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), \qquadα_1, α_2 \in\mathbb R \end{equation*} in the half-space ${\mathbb{R}}_{+}^{N+1}=\{(x,y):x\in {\mathbb{R}}^N,y>0\}$.

Portions of this article previously appeared as arXiv:2112.01791, which was split for publication