Harnack inequality for Bessel operators

Abstract

We prove uniqueness results and Harnack inequality for Bessel operators \begin{align*} %\label{def L transf alpha} D_t-Δ_{x} -2a\cdot\nabla_xD_y- D_{yy}- \frac cy D_y % \nonumber \\[1ex]&=y^α\sum_{i,j=1}^{N+1}a_{ij}D_{ij}+y^{α-1}\left(v,\nabla\right)-by^{α-2}. \end{align*} in the strip $[0,T]\times {\mathbb{R}}_{+}^{N+1}=\{0\le t\le T,x\in {\mathbb{R}}^N,y>0\}$ under Neumann boundary conditions at $y=0$.