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On the second Dirichlet eigenvalue of some nonlinear anisotropic elliptic operators.
- Source :
-
Bulletin des Sciences Mathematiques . Sep2019, Vol. 155, p10-32. 23p. - Publication Year :
- 2019
-
Abstract
- Let Ω be a bounded open set of R n , n ≥ 2. In this paper we mainly study some properties of the second Dirichlet eigenvalue λ 2 (p , Ω) of the anisotropic p -Laplacian − Q p u : = − div (F p − 1 (∇ u) F ξ (∇ u)) , where F is a suitable smooth norm of R n and p ∈ ] 1 , + ∞ [. We provide a lower bound of λ 2 (p , Ω) among bounded open sets of given measure, showing the validity of a Hong-Krahn-Szego type inequality. Furthermore, we investigate the limit problem as p → + ∞. [ABSTRACT FROM AUTHOR]
- Subjects :
- *NONLINEAR operators
*ELLIPTIC operators
*MEASURE theory
*NONLINEAR equations
Subjects
Details
- Language :
- English
- ISSN :
- 00074497
- Volume :
- 155
- Database :
- Academic Search Index
- Journal :
- Bulletin des Sciences Mathematiques
- Publication Type :
- Academic Journal
- Accession number :
- 138523115
- Full Text :
- https://doi.org/10.1016/j.bulsci.2019.02.005