SMOOTH EXHAUSTION FUNCTIONS IN CONVEX DOMAINS

Authors
BLOCKI Z
Citation
Z. Blocki, SMOOTH EXHAUSTION FUNCTIONS IN CONVEX DOMAINS, Proceedings of the American Mathematical Society, 125(2), 1997, pp. 477-484
Citations number
9
Categorie Soggetti
Mathematics, General",Mathematics,Mathematics
Journal title
Proceedings of the American Mathematical Society → ACNP
ISSN journal
00029939
Volume
125
Issue
2
Year of publication
1997
Pages
477 - 484
Database
ISI
SICI code
0002-9939(1997)125:2<477:SEFICD>2.0.ZU;2-D
Abstract
We show that in every bounded convex domain in R(n) there exists a smo oth convex exhaustion function psi such that the product of all eigenv alues of the matrix (partial derivative(2) psi/partial derivative x(j) partial derivative x(k)) is greater than or equal to 1. Moreover, if the domain is strictly convex, then psi can be chosen so that every ei genvalue is greater than or equal to 1.