Tomas Godoy, Jean-Pierre Gossez, Sofia R. Paczka
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.
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Tomas Godoy FAMAF, Univ. Nacional Córdoba Ciudad Universitaria, 5000 Córdoba, Argentina email: godoy@mate.uncor.edu |
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Jean-Pierre Gossez Département de Mathématique, C. P. 214 Université Libre de Bruxelles B-1050 Bruxelles, Belgium email: gossez@ulb.ac.be |
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Sofia Rosalia Paczka FAMAF, Univ. Nacional Córdoba Ciudad Universitaria, 5000 Córdoba, Argentina email: paczka@mate.uncor.edu |
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