An isoperimetric inequality for eigenvalues of the bi-harmonic operator

Details An isoperimetric inequality for eigenvalues of the bi-harmonic operator An isoperimetric inequality for eigenvalues of the bi-harmonic operator

2011-01-27

arxiv.org/abs/1101.5224v1

Mathematics

Analysis of PDEs

12 pages

Scientific paper

} In this article, we put forward a Neumann eigenvalue problem for the bi-harmonic operator $\Delta^2$ on a bounded smooth domain $\Om$ in the Euclidean $n$-space ${\bf R}^n$ ($n\ge2$) and then prove that the corresponding first non-zero eigenvalue $\Upsilon_1(\Om)$ admits the isoperimetric inequality of Szeg\"o-Weinberger type: $\Upsilon_1(\Om)\le \Upsilon_1(B_{\Om})$, where $B_{\Om}$ is a ball in ${\bf R}^n$ with the same volume of $\Om$. The isoperimetric inequality of Szeg\"o-Weinberger type for the first nonzero Neumann eigenvalue of the even-multi-Laplacian operators $\Delta^{2m}$ ($m\ge1$) on $\Om$ is also exploited.

Affiliated with

Also associated with

No associations

Rating

An isoperimetric inequality for eigenvalues of the bi-harmonic operator 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 An isoperimetric inequality for eigenvalues of the bi-harmonic operator, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An isoperimetric inequality for eigenvalues of the bi-harmonic operator will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-544683