The eigenvalue problem for the \(\infty \)-Bilaplacian

DOI10.1007/s00030-017-0492-4OpenAlexW2611111582MaRDI QIDQ1693408

Enea Parini, Nikolaos I. Katzourakis

Publication date: 31 January 2018

Published in: NoDEA. Nonlinear Differential Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1703.03648

zbMATH Keywords

differential inclusionsFaber-Krahn inequalitybathtub principlemulti-valued functions\(\infty \)-Laplacian\(\infty \)-Bilaplacian\(\infty \)-eigenvalue problemcalculus of variations in \(L^\infty \)symmetrisations

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Estimates of eigenvalues in context of PDEs (35P15) Boundary value problems for nonlinear higher-order PDEs (35G30) Nonlinear higher-order PDEs (35G20) Variational methods for eigenvalues of operators (49R05) Generalized solutions to partial differential equations (35D99) Viscosity solutions to PDEs (35D40) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)

Related Items (11)

Generalised vectorial \(\infty\)-eigenvalue nonlinear problems for \(L^{\infty}\) functionals ⋮ Structure and classification results for the ∞-elastica problem ⋮ Weak vs. 𝒟-solutions to linear hyperbolic first-order systems with constant coefficients ⋮ A relaxation result in the vectorial setting and power law approximation for supremal functionals ⋮ Variational Problems in L^∞ Involving Semilinear Second Order Differential Operators ⋮ Existence, uniqueness and structure of second order absolute minimisers ⋮ A minimisation problem in L^∞ with PDE and unilateral constraints ⋮ An $L^\infty$ Regularization Strategy to the Inverse Source Identification Problem for Elliptic Equations ⋮ Explicit \(\infty\)-harmonic functions in high dimensions ⋮ Inverse Optical Tomography through PDE Constrained Optimization $L^\infty$ ⋮ The streamlines of ∞-harmonic functions obey the inverse mean curvature flow

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