For every k ∈ N, we prove the existence of a quasi-open set minimizing the k-th eigenvalue
of the Dirichlet Laplacian among all sets of prescribed Lebesgue measure. Moreover, we …

We give a counterexample to the long standing conjecture that the ball maximises the first
eigenvalue of the Robin eigenvalue problem with negative parameter among domains of the …

We present some new bounds for the first Robin eigenvalue with a negative boundary
parameter. These include the constant volume problem, where the bounds are based on the …

We consider the problem of minimizing the k th eigenvalue of rectangles with unit area and
Dirichlet boundary conditions. This problem corresponds to finding the ellipse centred at the …

We study Schrödinger operators on compact finite metric graphs subject to $\delta $-
coupling and standard boundary conditions. We compare the $ n $-th eigenvalues of those …

In this paper we consider a Robin-type Laplace operator on bounded domains. We study the
dependence of its lowest eigenvalue on the boundary conditions and its asymptotic …

One of the principal topics of this paper concerns the realization of self-adjoint operators L Θ,
Ω in L 2 (Ω; dnx) m, m, n∈ ℕ, associated with divergence form elliptic partial differential …

Abstract Let Ω ⊂ R^ 2 Ω⊂ R 2 be a bounded planar domain, with piecewise smooth
boundary ∂ Ω∂ Ω. For σ> 0 σ> 0, we consider the Robin boundary value problem-Δ f= λ …

Let $\tau_k (\Omega) $ be the $ k $-th eigenvalue of the Laplace operator in a bounded
domain $\Omega $ of the form $\Omega_ {\text {out}}\setminus\overline {B_ {\alpha}} $ under …

We consider the problem of minimizing the kth Dirichlet eigenvalue of planar domains with
fixed perimeter and show that, as k goes to infinity, the optimal domain converges to the ball …