Complex and real valued solutions for fractoinal Helmholtz equation
Analysis of PDEs
2023-10-11 v2 Functional Analysis
Abstract
In this paper, we are concerned with the limiting absorption principle for the fractional Helmholtz equation, By establishing the boundedness estimate for the resolvent of fractional Helmholtz operator, we obtain the nontrivial Lq(Rn) complex valued solutions for (0.1). By setting up a dual variational framework, we also obtain the real valued solutions for (0.1) via a non-vanishing principle.
Cite
@article{arxiv.2309.13999,
title = {Complex and real valued solutions for fractoinal Helmholtz equation},
author = {Zifei Shen and Shuijin Zhang},
journal= {arXiv preprint arXiv:2309.13999},
year = {2023}
}
Comments
21pages. arXiv admin note: text overlap with arXiv:1402.3003 by other authors