On a fractional magnetic pseudorelativistic operator: properties and applications

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Bernini, Federico, d'Avenia, Pietro
Format: Preprint
Published: 2024
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866913567251365888
author Bernini, Federico
d'Avenia, Pietro
author_facet Bernini, Federico
d'Avenia, Pietro
contents We introduce a fractional magnetic pseudorelativistic operator for a general fractional order $s\in(0,1)$. First we define a suitable functional setting and we prove some fundamental properties. Then we show the behavior of the operator as $s \nearrow 1$ obtaining some results à la Bourgain-Brezis-Mironescu and removing the singularity from the integral definition. Finally we get existence of weak solutions for some semilinear equations involving a power type nonlinearity or a nonlocal (Choquard type) term.
format Preprint
id arxiv_https___arxiv_org_abs_2410_22426
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle On a fractional magnetic pseudorelativistic operator: properties and applications
Bernini, Federico
d'Avenia, Pietro
Analysis of PDEs
35S05, 35J61, 35Q60
We introduce a fractional magnetic pseudorelativistic operator for a general fractional order $s\in(0,1)$. First we define a suitable functional setting and we prove some fundamental properties. Then we show the behavior of the operator as $s \nearrow 1$ obtaining some results à la Bourgain-Brezis-Mironescu and removing the singularity from the integral definition. Finally we get existence of weak solutions for some semilinear equations involving a power type nonlinearity or a nonlocal (Choquard type) term.
title On a fractional magnetic pseudorelativistic operator: properties and applications
topic Analysis of PDEs
35S05, 35J61, 35Q60
url https://arxiv.org/abs/2410.22426