Document Type

Presentation

Publication Date

6-2014

Abstract

We study various lower and upper estimates for the first eigenvalue of Dirichlet Laplacians defined by positive Borel measures on bounded open subsets of Euclidean spaces. These Laplacians and the corresponding eigenvalue estimates differ from classical ones in that the defining measures can be singular. By using properties of self-similar measures, such as Strichartz's second-order self-similar identities, we improve some of the eigenvalue estimates.

Sponsorship/Conference/Institution

Cornell University Conference on Analysis, Probability and Mathematical Physics on Fractals

Location

Ithaca, NY

Source

http://www.math.cornell.edu/~fractals/5/ngai.pdf

Included in

Mathematics Commons

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