Existence of viscosity 1‑eigenpairs
Construct an appropriate 1‑limit eigenvalue formulation and prove (or refute) the existence of viscosity 1‑eigenpairs that are sharper than the generalized subgradient-based formulation for the $1$‑Laplacian eigenproblem.
References
The existence or not existence of viscosity 1-eigenpairs defined via some $1$-limit eigenequation sharper than the generalized eigenequation given in terms of subgradients (see \Cref{Def:generalized_p-eigenpair}), is currently an open problem.
— Nonlinear spectral graph theory
(Deidda et al., 4 Apr 2025) in Subsubsection 3.5, Viscosity p‑eigenpairs