Existence theorems for equations involving the 1-Laplacian: first eigenvalues for \(-\Delta_1\)

DOI10.1016/S1631-073X(02)02405-6zbMath1142.35408MaRDI QIDQ1608743

Francoise Demengel

Publication date: 8 August 2002

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

zbMATH Keywords

nontrivial solutionnecessary and sufficient conditionseigenvalue and eigenfunction

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Nonlinear elliptic equations (35J60)

Related Items (16)

BV supersolutions to equations of 1-Laplace and minimal surface type ⋮ A Neumann problem for the \(p(x)\)-Laplacian with \(p=1\) in a subdomain ⋮ Asymptotic behavior of the \(p\)-torsion functions as \(p\) goes to 1 ⋮ Asymptotic behavior related to Cheeger constant for solutions of an exponentially growth equation ⋮ On some weighted 1-Laplacian problem on \(\mathbb{R}^N\) with singular behavior at the origin ⋮ Existence and concentration behavior of solutions to 1-Laplace equations on \(\mathbb{R}^N\) ⋮ Elliptic equations involving the 1-Laplacian and a subcritical source term ⋮ On some nonlinear partial differential equations involving the 1-Laplacian ⋮ Generalized Cheeger sets related to landslides ⋮ Discontinuous velocity domain splitting in limit analysis ⋮ Approximation of maximal Cheeger sets by projection ⋮ On a weighted total variation minimization problem ⋮ A class of total variation minimization problems on the whole space ⋮ The limit as $p\to 1$ of the higher eigenvalues of the $p$-Laplacian operator $\Delta_p$ ⋮ THE SPECTRUM OF THE 1-LAPLACE OPERATOR ⋮ On a quasilinear elliptic problem involving the 1-biharmonic operator and a Strauss type compactness result

Cites Work

• The concentration-compactness principle in the calculus of variations. The limit case. I
• On semilinear elliptic equations with indefinite nonlinearities
• On some partial differential equation for non coercive functional and critical Sobolev exponent.
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