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.
Publié le : 1997-07-14
Classification:
Principal eigenvalues,
quantitative Wiener criterion,
enlargement of obstacles,
60J45,
35P15,
82D30
@article{1024404510,
author = {Sznitman, Alain-Sol},
title = {Capacity and principal eigenvalues: the method of enlargement of
obstacles revisited},
journal = {Ann. Probab.},
volume = {25},
number = {4},
year = {1997},
pages = { 1180-1209},
language = {en},
url = {http://dml.mathdoc.fr/item/1024404510}
}
Sznitman, Alain-Sol. Capacity and principal eigenvalues: the method of enlargement of
obstacles revisited. Ann. Probab., Tome 25 (1997) no. 4, pp. 1180-1209. http://gdmltest.u-ga.fr/item/1024404510/