Isoperimetric Inequality for degenerate elliptic operators of Grushin type

Dangyang He

Let $n,m\ge 1$, $\alpha \in (0,1)$, and $\beta \ge 0$. For the Grushin-type operator \[ L=-\nabla_x\!\cdot\!\bigl(|x|^{2α}\nabla_x\bigr)+|x|^{2β}Δ_y \qquad \text{on } \mathbb R^n\times \mathbb…