On the second anisotropic Cheeger constant and related questions

2025/03/29 by Piscitelli, Gianpaolo
#47J10 - 49Q20 - 52A38 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.23092

Abstract

In this paper we study the behavior of the second eigenfunction of the anisotropic p-Laplace operator - Q_pu:=-\textrmdiv (F^p-1(∇ u)F_ξ(∇ u)), as p → 1⁺, where F is a suitable smooth norm of \mathbb Rⁿ. Moreover, for any regular set Ω, we define the second anisotropic Cheeger constant as h_2,F(Ω):=inf \ max\\fracP_F(E₁)|E₁|,\fracP_F(E₂)|E₂|\, E₁,E₂⊂ Ω, E₁∩ E₂=∅\, where P_F(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.

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