Some special aspects related to the 1-Laplace operator

DOI10.1515/ACV.2010.021zbMath1211.35214MaRDI QIDQ3074549

Zoja Milbers, Friedemann Schuricht

Publication date: 9 February 2011

Published in: Advances in Calculus of Variations (Search for Journal in Brave)

zbMATH Keywords

generalized solutionseigenvalue problem1-Laplace operator

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Variational methods for eigenvalues of operators (49R05) Representations of solutions to partial differential equations (35C99) Qualitative properties of solutions to partial differential equations (35B99) Generalized solutions to partial differential equations (35D99)

Related Items (max. 100)

Convergence of the eigenvalues of the \(p\)-Laplace operator as \(p\) goes to 1 ⋮ Necessary condition for eigensolutions of the 1-Laplace operator by means of inner variations ⋮ On an isoperimetric problem with power-law potentials and external attraction ⋮ 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 ⋮ First eigenfunctions of the 1-Laplacian are viscosity solutions

Cites Work

• An alternative derivation of the eigenvalue equation for the 1-Laplace operator
• Minimal boundaries enclosing a given volume
• On the equation of surfaces of prescribed mean curvature. Existence and uniqueness without boundary conditions
• Characterization of Cheeger sets for convex subsets of the plane
• C1 + α local regularity of weak solutions of degenerate elliptic equations
• DIRICHLET PROBLEMS FOR THE 1-LAPLACE OPERATOR, INCLUDING THE EIGENVALUE PROBLEM
• Functions locally almost 1-harmonic
• Uniqueness of the Cheeger set of a convex body

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