Optimal domains for elliptic eigenvalue problems with rough coefficients

Smoothness and regularity of solutions to PDEs (35B65) Boundary value problems for second-order elliptic equations (35J25) General topics in linear spectral theory for PDEs (35P05) Optimization of shapes other than minimal surfaces (49Q10) Variational methods for second-order elliptic equations (35J20)

Cites Work

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Existence of minimizers for spectral problems
Spectral optimization problems
An existence result for a class of shape optimization problems
Minimization problems for eigenvalues of the Laplacian.
Minimizing the second eigenvalue of the Laplace operator with Dirichlet boundary conditions
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.
Elliptic partial differential equations of second order
Minimization of the \(k\)-th eigenvalue of the Dirichlet Laplacian
Lipschitz continuity of state functions in some optimal shaping
Sharp regularity for general Poisson equations with borderline sources
Maximization of the second non-trivial Neumann eigenvalue
Regularity of optimal sets for some functional involving eigenvalues of an operator in divergence form
Existence and regularity of Faber-Krahn minimizers in a Riemannian manifold
Lipschitz regularity of the eigenfunctions on optimal domains
Regularity of the optimal shape for the first eigenvalue of the Laplacian with volume and inclusion constraints
Existence and regularity of optimal shapes for elliptic operators with drift
Variational methods in shape optimization problems
Regularity of the optimal sets for the second Dirichlet eigenvalue
An Optimization Problem with Volume Constraint
Regularity for Shape Optimizers: The Nondegenerate Case
Free boundary problems involving singular weights
Regularity for Shape Optimizers: The Degenerate Case
Optimal Shape Problems for Eigenvalues
Lipschitz continuity of the eigenfunctions on optimal sets for functionals with variable coefficients
On a constrained variational problem with an arbitrary number of free boundaries
Quantitative homogenization of principal Dirichlet eigenvalue shape optimizers