In this paper we study the behavior of the second eigenfunction of the anisotropic p-Laplace operator −Qpu := − div F p−1 (∇u)Fξ(∇u)  , as p → 1+, where F is a suitable smooth norm of Rn. Moreover, for any regular set Ω, we define the second anisotropic Cheeger constant as h2,F (Ω) := inf  max  PF (E1) |E1| , PF (E2) |E2|  , E1, E2 ⊂ Ω, E1 ∩ E2 = ∅  , where PF (E) is the anisotropic perimeter of E, and study the connection with the second eigenvalue of the anisotropic p-Laplacian. Finally, we study the twisted anisotropic q-Cheeger constant with a volume constraint
On the second anisotropic Cheeger constant and related questions
G. Piscitelli
2026-01-01
Abstract
In this paper we study the behavior of the second eigenfunction of the anisotropic p-Laplace operator −Qpu := − div F p−1 (∇u)Fξ(∇u) , as p → 1+, where F is a suitable smooth norm of Rn. Moreover, for any regular set Ω, we define the second anisotropic Cheeger constant as h2,F (Ω) := inf max PF (E1) |E1| , PF (E2) |E2| , E1, E2 ⊂ Ω, E1 ∩ E2 = ∅ , where PF (E) is the anisotropic perimeter of E, and study the connection with the second eigenvalue of the anisotropic p-Laplacian. Finally, we study the twisted anisotropic q-Cheeger constant with a volume constraintFile in questo prodotto:
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