A negative result on regularity estimates on finite radial Morse index solutions to elliptic problems
Analysis of PDEs
2024-04-11 v1
Abstract
In the regularity theory of solutions to elliptic partial differential equations often the concept of stability plays the role of a sufficient condition for smoothness. It is a natural question to ask if this holds true for nonstable but finite Morse index solutions. We provide a negative answer showing the existence of sequences of solutions with radial Morse index equal to 1 for which regularity estimates can not be satisfied.
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Cite
@article{arxiv.2404.06944,
title = {A negative result on regularity estimates on finite radial Morse index solutions to elliptic problems},
author = {J. Silverio Martinez-Baena and Salvador Villegas},
journal= {arXiv preprint arXiv:2404.06944},
year = {2024}
}
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8 pages