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The first Grushin eigenvalue on cartesian product domains.
The first Grushin eigenvalue on cartesian product domains.
- Source :
-
Advances in Calculus of Variations . Apr2024, Vol. 17 Issue 2, p353-371. 19p. - Publication Year :
- 2024
-
Abstract
- In this paper, we consider the first eigenvalue λ 1 (Ω) of the Grushin operator Δ G := Δ x 1 + | x 1 | 2 s Δ x 2 with Dirichlet boundary conditions on a bounded domain Ω of ℝ d = ℝ d 1 + d 2 . We prove that λ 1 (Ω) admits a unique minimizer in the class of domains with prescribed finite volume, which are the cartesian product of a set in ℝ d 1 and a set in ℝ d 2 , and that the minimizer is the product of two balls Ω 1 * ⊆ ℝ d 1 and Ω 2 * ⊆ ℝ d 2 . Moreover, we provide a lower bound for | Ω 1 * | and for λ 1 (Ω 1 * × Ω 2 *) . Finally, we consider the limiting problem as s tends to 0 and to + ∞ . [ABSTRACT FROM AUTHOR]
- Subjects :
- *EIGENVALUES
*SCHRODINGER operator
Subjects
Details
- Language :
- English
- ISSN :
- 18648258
- Volume :
- 17
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Advances in Calculus of Variations
- Publication Type :
- Academic Journal
- Accession number :
- 176386411
- Full Text :
- https://doi.org/10.1515/acv-2022-0015