涉及伪相对论薛定谔算子的抛物方程的渐近特性

Pub Date : 2024-06-01 DOI:10.1007/s10255-024-1097-4

Chen Qiao, Su-fang Tang

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引用次数: 0

摘要

本文研究了涉及非局部伪相对论薛定谔算子 (-Δ + m2)s 的抛物方程，其中 s∈ (0, 1) 和质量 m > 0 在有界区域内。我们建立了反对称函数的渐近窄区原理和渐近强最大原理。作为应用，我们利用移动平面的方法，证明了单位球内正解的渐近径向对称性和单调性。

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Asymptotic Property of Parabolic Equations Involving Pseudo-relativistic Schrödinger Operators

In this paper, we investigate parabolic equations involving nonlocal pseudo-relativistic Schrödinger operators (−Δ + m²)^s with s ∈ (0, 1) and mass m > 0 in bounded regions. We establish the asymptotic narrow region principle and asymptotic strong maximum principle for anti symmetric function. As applications, employing the method of moving planes, we show the asymptotical radial symmetry and monotonicity of positive solutions in an unit ball.

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