Kernel estimates for Schrödinger type operators with unbounded diffusion and potential terms

Anna Canale, Abdelaziz Rhandi, Cristian Tacelli

We prove that the heat kernel associated to the Schrödinger type operator $A:=(1+|x{|}^{\alpha })\Delta -|x{|}^{\beta }$ satisfies the estimate $$k(t,x,y)\leq c_1e^{λ_0t}e^{c_2t^{-b}}\frac{(|x||y|)^{-\frac…