Lower Bounds on Eigenfunctions and the First Eigenvalue Gap

R. M. Brown, P. D. Hislopt, A. Martinez

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We give upper and lower bounds on the difference ΔE ≡E2 −E1, of the first two Dirichlet eigenvalues for a dumbbell region in Rn. These bounds are exponentially small in the diameter ɛ of the straight tube connecting two identical bounded cavities as ɛ → 0. The proof relies on a lower bound for the first Dirichlet eigenfunction for one cavity with a thin tube attached.

Original languageEnglish
Pages (from-to)33-49
Number of pages17
JournalMathematics in Science and Engineering
Issue numberC
StatePublished - Jan 1 1993

Bibliographical note

Funding Information:
*Supported in part by NSF DMS 91-03046. 'Supported in part by NSF DMS 91-06479 and INT 90-15895.

ASJC Scopus subject areas

  • General Mathematics
  • General Engineering


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