On the fractional relativistic Schrödinger operator
type: Item
instance of: scholarly article
title: On the fractional relativistic Schrödinger operator
zbMATH Open document ID: 1495.47074
author: Vincenzo Ambrosio
published in: Journal of Differential Equations
publication date: 2021-11-30T00:00:00Z
review text: This paper concerns the fractional relativistic Schrödinger equation defined by \((-\Delta+m^2)^su=g(x,u)\in \mathbb{R}^N\). Several works have recently shown some interesting results regarding existence and multiplicity of solutions for the equation. In this paper, the author analyzes specific behaviors of the solutions such as regularity, decay, and symmetry. To be specific, the results include \(L^\infty\)- regularity, exponential decay, a~Pohozaev-type identity, and the radial symmetry of the solutions. The results in this paper are established by exploiting fractional Sobolev spaces and properties of Bessel functions.
reviewed by: Miyeon Kwon
Mathematics Subject Classification ID: 47G30
Mathematics Subject Classification ID: 35R11
Mathematics Subject Classification ID: 42B35
Mathematics Subject Classification ID: 35B09
zbMATH DE Number: 7436215
zbMATH Keywords: fractional relativistic operators
zbMATH Keywords: Kato's inequality
zbMATH Keywords: regularity results
zbMATH Keywords: exponential decay
zbMATH Keywords: Pohozaev identity
zbMATH Keywords: radial symmetry
MaRDI profile type: Publication
full work available at URL: j.jde.2021.07.048
OpenAlex ID: W3215845959
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DOI: 10.1016/J.JDE.2021.07.048
description: scientific article; zbMATH DE number 7436215