THE SPECTRUM OF THE 1-LAPLACE OPERATOR

DOI10.1142/S0219199709003570zbMath1182.35175MaRDI QIDQ3648317

Kung-Ching Chang

Publication date: 25 November 2009

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

zbMATH Keywords

nonlinear eigenvalue problemnonsmooth critical point theory1-Laplace operatorbounded variation function

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Degenerate elliptic equations (35J70) Nonlinear spectral theory, nonlinear eigenvalue problems (47J10)

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Cites Work

• The total variation flow in \(\mathbb R^N\)
• Variational methods for non-differentiable functionals and their applications to partial differential equations
• Buckling of nonlinearly elastic rods in the presence of obstacles treated by nonsmoth critical point theory
• A critical point theory for nonsmooth functionals
• A general approach to the min-max principle
• Parabolic quasilinear equations minimizing linear growth functionals
• Some qualitative properties for the total variation flow
• Existence theorems for equations involving the 1-Laplacian: first eigenvalues for \(-\Delta_1\)
• Stability and perturbations of the domain for the first eigenvalue of the 1-Laplacian
• DIRICHLET PROBLEMS FOR THE 1-LAPLACE OPERATOR, INCLUDING THE EIGENVALUE PROBLEM
• Functions locally almost 1-harmonic
• On Some Nonlinear Partial Differential Equations Involving the “1”-Laplacian and Critical Sobolev Exponent
• Explicit Solutions of the Eigenvalue Problem $div \left(\frac Du\vert Du \vert \right)=u$ in $R^2$

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