A numerical investigation of level sets of extremal Sobolev functions
Numerical Analysis
2016-01-20 v1 Analysis of PDEs
Abstract
In this paper we investigate the level sets of extremal Sobolev functions for subcritical exponents p. We conjecture that as p increases the corresponding extremal functions become more peaked, which we can measure by comparing their distribution functions. Then we provide compelling numerical evidence for our conjecture.
Keywords
Cite
@article{arxiv.1401.2313,
title = {A numerical investigation of level sets of extremal Sobolev functions},
author = {Stefan Juhnke and Jesse Ratzkin},
journal= {arXiv preprint arXiv:1401.2313},
year = {2016}
}
Comments
15 pages, 9 figures, submitted