2006 International Conference in Honor of Jacqueline Fleckinger.
Electronic Journal of Differential Equations,
Conference 16 (2007), pp. 137-154.
Title: A minimax formula for the principal eigenvalues
of Dirichlet problems and its applications
Authors: Tomas Godoy (Univ. Nacional Cordoba, Argentina)
Jean-Pierre Gossez (Univ. Libre de Bruxelles, Belgium)
Sofia R. Paczka (Univ. Nacional Cordoba, Argentina)
Abstract:
A minimax formula for the principal eigenvalue of a nonselfadjoint
Dirichlet problem was established in [8,18]. In this paper we
generalize this formula to the case where an indefinite weight is
present. Our proof requires less regularity and, unlike that in
[8,18], does not rely on semigroups theory nor on stochastic
differential equations. It makes use of weighted Sobolev spaces.
An application is given to the study of the uniformity of the
antimaximum principle.
Published May 15, 2007.
Math Subject Classifications: 35J20, 35P15.
Key Words: Nonselfadjoint elliptic problem; principal eigenvalue;
indefinite weight; minimax formula; weighted Sobolev spaces;
degenerate elliptic equations; antimaximum principle.