Existence of bubbling solutions without mass concentration
Analysis of PDEs
2018-07-13 v1
Abstract
The seminal work \cite{bm} by Brezis and Merle has been pioneering in studying the bubbling phenomena of the mean field equation with singular sources. When the vortex points are not collapsing, the mean field equation possesses the property of the so-called "bubbling implies mass concentration". Recently, Lin and Tarantello in \cite{lt} pointed out that the "bubbling implies mass concentration" phenomena might not hold in general if the collapse of singularities occurs. In this paper, we shall construct the first concrete example of non-concentrated bubbling solution of the mean field equation with collapsing singularities.
Cite
@article{arxiv.1807.04432,
title = {Existence of bubbling solutions without mass concentration},
author = {Youngae Lee and Chang-Shou Lin and Wen Yang},
journal= {arXiv preprint arXiv:1807.04432},
year = {2018}
}
Comments
This paper will appear at Annales de l'Institut Fourier