A variational characterisation of the second eigenvalue of the p‐Laplacian on quasi open sets

DOI10.1112/plms.12240zbMath1423.35288arXiv1806.07303OpenAlexW3101312310MaRDI QIDQ5237453

Yi Ru-Ya Zhang, Shirsho Mukherjee, Nicola Fusco

Publication date: 18 October 2019

Published in: Proceedings of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.07303

zbMATH Keywords

\(p\)-Laplaciansecond eigenvaluequasi-open setminimax characterisation

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Variational principles in infinite-dimensional spaces (58E30) Optimization of shapes other than minimal surfaces (49Q10) Variational methods for second-order elliptic equations (35J20)

Related Items (7)

The Dirichlet problem for \(p\)-minimizers on finely open sets in metric spaces ⋮ Convergence and local-to-global results for \(p\)-superminimizers on quasiopen sets ⋮ Removable sets for Newtonian Sobolev spaces and a characterization of \(p\)-path almost open sets ⋮ Optimization of nonlinear eigenvalues under measure or perimeter constraint ⋮ Optimization results for the higher eigenvalues of the p‐Laplacian associated with sign‐changing capacitary measures ⋮ Unnamed Item ⋮ A uniqueness result for functions with zero fine gradient on quasiconnected and finely connected sets

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