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.
Original language | American English |
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State | Published - Jun 1 2014 |
Event | Cornell University Conference on Analysis, Probability and Mathematical Physics on Fractals - Duration: Jun 1 2014 → … |
Conference
Conference | Cornell University Conference on Analysis, Probability and Mathematical Physics on Fractals |
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Period | 06/1/14 → … |
Disciplines
- Mathematics
- Physical Sciences and Mathematics
Keywords
- Borel probability measure
- Dirichlet Laplacian
- Eigenfunctions
- Eigenvalues
- Poincare type inequality