Year: 2013
Type: preprint
Abstract: This paper estimates the location and the width of the nodal set of the first Neumann eigenfunctions on a smooth convex domain $Ω\subset \mathbb R^n$, whose length is normalized to be 1 and whose cross-section is contained in a ball of radius $ε$. In \cite{CJK2009}, an $O(ε)$ bound was obtained by constructing a coordinate system. In this paper, we present a simpler method that does not require such a coordinate system. Moreover, in the special case $n = 2$, we obtain an $O(ε^2)$ bound on the width of the nodal set, in analogy to the corresponding result in the Dirichlet case obtained in \cite{GJ1995}.
Source: arXiv (Cornell University)
Author: Zheng, Fan
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2245075092