A phase-field version of the Faber-Krahn theorem

Boundary value problems for second-order elliptic equations (35J25) General topics in linear spectral theory for PDEs (35P05) Estimates of eigenvalues in context of PDEs (35P15) Optimization of shapes other than minimal surfaces (49Q10) Variational methods for eigenvalues of operators (49R05)

Cites Work

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Linear functional analysis. An application-oriented introduction. Translated from the 6th German edition by Robert Nürnberg
Existence of minimizers for spectral problems
Faber-Krahn inequalities for the Robin-Laplacian: a free discontinuity approach
An alternative approach to the Faber-Krahn inequality for Robin problems
The effect of a singular perturbation on nonconvex variational problems
An optimal design problem with perimeter penalization
Über eine von Rayleigh formulierte Minimaleigenschaft des Kreises.
Beweis, daß unter allen homogenen Membranen von gleicher Fläche und gleicher Spannung die kreisförmige den tiefsten Grundton gibt.
Regularity of minimizers of shape optimization problems involving perimeter
Shape variation and optimization. A geometrical analysis
The gradient theory of phase transitions and the minimal interface criterion
A selection principle for the sharp quantitative isoperimetric inequality
Shape and topology optimization involving the eigenvalues of an elastic structure: a multi-phase-field approach
Maximization of the second non-trivial Neumann eigenvalue
Faber-Krahn inequalities in sharp quantitative form
The sharp quantitative isoperimetric inequality
A Faber-Krahn inequality for Robin problems in any space dimension
Maximization of Neumann eigenvalues
Analysis.
Qualitative and numerical analysis of a spectral problem with perimeter constraint
Sets of finite perimeter and geometric variational problems. An introduction to geometric measure theory
A free boundary approach to shape optimization problems
Minimizers and gradient flows for singularly perturbed bi-stable potentials with a Dirichlet condition
Stability estimates for certain Faber-Krahn,isocapacitary and Cheeger inequalities
The Cahn–Hilliard gradient theory for phase separation with non-smooth free energy Part I: Mathematical analysis
Elliptic Partial Differential Equations of Second Order
Design-dependent loads in topology optimization
A free boundary approach to the Faber-Krahn inequality
Minimization of $\lambda_{2}(\Omega)$ with a perimeter constraint
Isoperimetric Inequalities in Mathematical Physics. (AM-27)
Phase-field methods for spectral shape and topology optimization
Calculus of variations
On the polygonal Faber-Krahn inequality