Optimal kernel estimates for a Schrödinger type operator

2016/04/13 by Anna Canale, Canale, Anna, Cristian Tacelli +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #math.AP

paper · pdf · doi:10.48550/arxiv.1604.03960

arxiv created 2016/04/13 · openalex publication_date 2016/04/13 · arxiv updated 2016/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 0<t<1, provided that N>2, 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.

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