Optimal kernel estimates for a Schrödinger type operator

2016/04/13 by Canale, Anna, Tacelli, Cristian
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1604.03960

Abstract

In the paper the principal result obtained is the estimate for the heat kernel associated to the Schrödinger type operator (1+|x|^α)Δ-|x|^β k(t,x,y)≤ Ct^-\fracθ2\frac φ(x)φ(y)1+|x|^α, where φ=(1+|x|^α)^(2-θ)/(4)+\frac1α(θ-N)/(2), θ≥ N and 02, α> 2 and β>α-2. This estimate improves a similar estimate in \cite can-rhan-tac2 with respect to the dependence on spatial component.

Related

• Kernel estimates for Schrödinger type operators with unbounded diffusion and potential terms
• Critical heat kernel estimates via Hardy-Sobolev inequalities
• Sharp two-sided heat kernel estimates for Schrödinger operators with decaying potentials
• Sharp Gaussian estimates for heat kernels of Schrödinger operators
• Schroedinger Operator: Heat Kernel and Its Applications