Large time behavior of solutions of the heat equation with inverse square potential

Abstract

Let $L:=-\Delta +V$ be a nonnegative Schrödinger operator on $L^2({\mathbf{R}}^N)$, where $N\ge 2$ and $V$ is a radially symmetric inverse square potential. In this paper we assume either $L$ is subcritical or null-critical and we establish a method for obtaining the precise description of the large time behavior of $e^{-tL}\phi$, where $\phi \in L^2({\mathbf{R}}^N,e^{|x{|}^2/4}dx)$.

References in corpus (1)

• Sharp decay estimates in Lorentz spaces for nonnegative Schrödinger heat semigroups

Cited by in corpus (1)

• Hot spots of solutions to the heat equation with inverse square potential