Abstract

We study the behavior of the second eigenfunction of the anisotropic pp-Laplace operator −Qpu:=−div(Fp−1(∇u)Fξ(∇u)),-\mathcal Q_{p}u:=-{\rm div} \left(F^{p-1}(\nabla u)F_\xi (\nabla u)\right), as p→1+p \to 1^+, where FF is a suitable smooth norm of Rn\mathbb{R}^{n}. Moreover, for any regular set Ω\Omega, we define the second anisotropic Cheeger constant as h2,F(Ω):=inf⁡{max⁡{PF(E1)∣E1∣,PF(E2)∣E2∣},  E1,E2⊂Ω,E1∩E2=∅},h_{2,F}(\Omega):=\inf \left\{ \max\left\{\frac{P_{F}(E_{1})}{|E_{1}|},\frac{P_{F}(E_{2})}{|E_{2}|}\right\},\; E_{1},E_{2}\subset \Omega, E_{1}\cap E_{2}=\emptyset\right\}, where PF(E)P_{F}(E) is the anisotropic perimeter of EE, and study the connection with the second eigenvalue of the anisotropic pp-Laplacian. Finally, we study the twisted anisotropic qq-Cheeger constant with a volume constraint.

Author information

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Keywords

  • Nonlinear eigenvalue problems
  • second anisotropic Cheeger constant
  • second eigenfunctions of the p-Laplacian

Mathematics Subject Classification

47J10, 49Q20, 52A38

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Suggested citation

G. Piscitelli. “On the Second Anisotropic Cheeger Constant and Related Questions.” Journal of Convex Analysis 33 (2026), No. 1&2, 303–324. https://doi.org/10.68381/jca33019

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Published by Heldermann Verlag, 2026. Rights now held by Banach Press LLC.