Necessary condition for eigensolutions of the 1-Laplace operator by means of inner variations

DOI10.1007/s00208-012-0829-6zbMath1267.35150OpenAlexW2081741845MaRDI QIDQ1952281

Zoja Milbers, Friedemann Schuricht

Publication date: 30 May 2013

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00208-012-0829-6

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Variational methods for eigenvalues of operators (49R05)

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\(p\)-Laplace operators for oriented hypergraphs, Convergence of the eigenvalues of the \(p\)-Laplace operator as \(p\) goes to 1, The convective eigenvalues of the one-dimensional \(p\)-Laplacian as \(p\rightarrow 1\), The limit as $p\to 1$ of the higher eigenvalues of the $p$-Laplacian operator $\Delta_p$, Perturbation results involving the 1-Laplace operator, The Cheeger N-problem in terms of BV functions, \(p\)-Laplacian diffusion coupled to logistic reaction: asymptotic behavior as \(p\) goes to 1. To the memory of Professor Ireneo Peral Alonso, a brilliant mathematician, excellent person and dear friend, First eigenfunctions of the 1-Laplacian are viscosity solutions

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