Asymptotic First Eigenvalue Estimates for the Biharmonic Operator on a Rectangle
Spectral Theory
2007-05-23 v1 Functional Analysis
Abstract
We find an asymptotic expression for the first eigenvalue of the biharmonic operator on a long thin rectangle. This is done by finding lower and upper bounds which become increasingly accurate with increasing length. The lower bound is found by algebraic manipulation of the operator, and the upper bound is found by minimising the quadratic form for the operator over a test space consisting of separable functions. These bounds can be used to show that the negative part of the groundstate is small.
Cite
@article{arxiv.math/9803011,
title = {Asymptotic First Eigenvalue Estimates for the Biharmonic Operator on a Rectangle},
author = {Mark P. Owen},
journal= {arXiv preprint arXiv:math/9803011},
year = {2007}
}
Comments
27 pages, 4 diagrams, 2 tables