On the Hardy-Littlewood-Sobolev type systems
Analysis of PDEs
2015-10-13 v2
Abstract
In this paper, we study some qualitative properties of Hardy-Littlewood-Sobolev type systems. The HLS type systems are categorized into three cases: critical, supercritical and subcritical. The critical case, the well known original HLS system, corresponds to the Euler-Lagrange equations of the fundamental HLS inequality. In each case, we give a brief survey on some important results and useful methods. Some simplifications and extensions based on somewhat more direct and intuitive ideas are presented. Also, a few new qualitative properties are obtained and several open problems are raised for future research.
Keywords
Cite
@article{arxiv.1509.06822,
title = {On the Hardy-Littlewood-Sobolev type systems},
author = {Ze Cheng and Genggeng Huang and Congming Li},
journal= {arXiv preprint arXiv:1509.06822},
year = {2015}
}