Dirichlet Heat Kernel Estimates for ${\Delta }^{\alpha /2}+{\Delta }^{\beta /2}$

Zhen-Qing Chen, Panki Kim, Renming Song

For $d\ge 1$ and $0<\beta <\alpha <2$, consider a family of pseudo differential operators $\{{\Delta }^{\alpha }+a^{\beta }{\Delta }^{\beta /2};a\in [0,1]\}$ that evolves continuously from ${\Delta }^{\alpha /2}$ to ${\Delta }^{\alpha /2}+{\Delta }^{\beta /2}$…