On a new type of Inequality related to the Uniform Sublevel Set Problem
Classical Analysis and ODEs
2020-05-20 v1
Abstract
Recently, Steinerberger proved a uniform inequality for the Laplacian serving as a counterpoint to the standard uniform sublevel set inequality which is known to fail for the Laplacian. In this note, we give an elementary proof of this result which highlights a step allowing for adaptations to other situations, for instance, we show that the inequality also holds for the heat operator. We formulate some naturally arising questions.
Cite
@article{arxiv.2005.09407,
title = {On a new type of Inequality related to the Uniform Sublevel Set Problem},
author = {John Green},
journal= {arXiv preprint arXiv:2005.09407},
year = {2020}
}
Comments
25 pages, 0 figures