SOME ESTIMATES FOR THE SYMMETRIZED FIRST EIGENFUNCTION OF THE LAPLACIAN

Authors
BHATTACHARYA T WEITSMAN A
Citation
T. Bhattacharya et A. Weitsman, SOME ESTIMATES FOR THE SYMMETRIZED FIRST EIGENFUNCTION OF THE LAPLACIAN, Potential analysis, 9(2), 1998, pp. 143-172
Citations number
10
Categorie Soggetti
Mathematics,Mathematics
Journal title
Potential analysis → ACNP
ISSN journal
09262601
Volume
9
Issue
2
Year of publication
1998
Pages
143 - 172
Database
ISI
SICI code
0926-2601(1998)9:2<143:SEFTSF>2.0.ZU;2-0
Abstract
In this paper a method is developed to study the first eigenfunction u > 0 of the Laplacian. It is based on a study of the distribution func tion for u. The distribution function satisfies an integrodifferential inequality, and by introducing a maximal solution Z of the correspond ing equation, bounds obtained for Z are then used to estimate u. These bounds come from a detailed study of Z, especially the basic identity derived in Theorem 3.1.