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Sharp Bounds for Ground State Eigenfunctions on Domains with Horns and Cusps

✍ Scribed by A Lindeman II; M.H Pang†; Z Zhao‡


Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
353 KB
Volume
212
Category
Article
ISSN
0022-247X

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✦ Synopsis


We prove a lower bound on the ground state eigenfunction of the Dirichlet Laplacian for horn-shaped and cusped domains. The novelty of the method is that for horn-shaped domains it implies a new result for dimension two, and more importantly, is valid for higher dimensions. Moreover, the same technique applies just as easily to cusps. Finally, we construct an example to show that the estimates are sharp.