Asymptotic First Eigenvalue Estimates for the Biharmonic Operator on a Rectangle

Details Asymptotic First Eigenvalue Estimates for the Biharmonic Operator on a Rectangle Asymptotic First Eigenvalue Estimates for the Biharmonic Operator on a Rectangle

1998-03-05

arxiv.org/abs/math/9803011v1

Journal of Differential Equations. Vol. 136, No. 1, (1997)

Mathematics

Spectral Theory

27 pages, 4 diagrams, 2 tables

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Asymptotic First Eigenvalue Estimates for the Biharmonic Operator on a Rectangle does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Asymptotic First Eigenvalue Estimates for the Biharmonic Operator on a Rectangle, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Asymptotic First Eigenvalue Estimates for the Biharmonic Operator on a Rectangle will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-679763