Geometrical Versions of improved Berezin-Li-Yau Inequalities

Details Geometrical Versions of improved Berezin-Li-Yau Inequalities Geometrical Versions of improved Berezin-Li-Yau Inequalities

2010-10-13

arxiv.org/abs/1010.2683v1

Journal of Spectral Theory 1 (2011), no. 1, 87-109

Mathematics

Spectral Theory

18 pages, 1 figure

Scientific paper

We study the eigenvalues of the Dirichlet Laplace operator on an arbitrary bounded, open set in $\R^d$, $d \geq 2$. In particular, we derive upper bounds on Riesz means of order $\sigma \geq 3/2$, that improve the sharp Berezin inequality by a negative second term. This remainder term depends on geometric properties of the boundary of the set and reflects the correct order of growth in the semi-classical limit. Under certain geometric conditions these results imply new lower bounds on individual eigenvalues, which improve the Li-Yau inequality.

Affiliated with

Also associated with

No associations

Rating

Geometrical Versions of improved Berezin-Li-Yau Inequalities 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 Geometrical Versions of improved Berezin-Li-Yau Inequalities, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Geometrical Versions of improved Berezin-Li-Yau Inequalities will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-226885