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
In corso di stampa
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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