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July 1997 Capacity and principal eigenvalues: the method of enlargement of obstacles revisited
Alain-Sol Sznitman
Ann. Probab. 25(3): 1180-1209 (July 1997). DOI: 10.1214/aop/1024404510


We describe a coarse graining method, which provides lower bounds on the principal Dirichlet eigenvalue of the Laplacian in regions receiving small obstacles, and sharpens the previous method of enlargement of obstacles. Based on a quantitative Wiener criterion, one replaces the actual obstacles by obstacles of a much larger size. Controls on the shift of principal eigenvalues and capacity estimates on the locus where the Wiener criterion breaks down are derived. The results are written in a self-contained fashion.


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Alain-Sol Sznitman. "Capacity and principal eigenvalues: the method of enlargement of obstacles revisited." Ann. Probab. 25 (3) 1180 - 1209, July 1997.


Published: July 1997
First available in Project Euclid: 18 June 2002

zbMATH: 0885.60063
MathSciNet: MR1457616
Digital Object Identifier: 10.1214/aop/1024404510

Primary: 35P15 , 60J45 , 82D30

Keywords: enlargement of obstacles , principal eigenvalues , quantitative Wiener criterion

Rights: Copyright © 1997 Institute of Mathematical Statistics


Vol.25 • No. 3 • July 1997
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