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 consider the Laplacian on a class of smooth domains Ω⊂ R ν, ν≥ 2, with attractive
Robin boundary conditions: Q α Ω u=− Δ u,∂ u∂ n= α u on∂ Ω, α> 0, where n is the outer …

We consider the Laplacian with attractive Robin boundary conditions, Q^ Ω _ α u=-Δ u,\quad
∂ u ∂ n= α u on ∂ Ω, Q α Ω u=-Δ u,∂ u∂ n= α u on∂ Ω, in a class of bounded smooth …

Shape optimization conjectures for the first two eigenvalues of the Robin Laplacian are
developed and supported with new results for rectangular boxes. The square minimizes the …

Robin problem for the Laplacian in a bounded planar domain with a smooth boundary and a
large parameter in the boundary condition is considered. We prove a two-sided three-term …

Abstract Let Ω ⊂ R^ ν Ω⊂ R ν, ν ≥ 2 ν≥ 2, be a C^ 1, 1 C 1, 1 domain whose boundary ∂
Ω∂ Ω is either compact or behaves suitably at infinity. For p ∈ (1, ∞) p∈(1,∞) and α> 0 α> …

For a bounded corner domain Ω, we consider the attractive Robin Laplacian in Ω with large
Robin parameter. Exploiting multiscale analysis and a recursive procedure, we have a …

Let Ω⊂ R 2 be a domain having a compact boundary Σ which is Lipschitz and piecewise C 4
smooth, and let ν denote the inward unit normal vector on Σ. We study the principal …

On the Discrete Spectrum of Robin Laplacians in Conical Domains Page 1 “cone18-mmnp” —
2016/2/26 — 21:23 — page 100 — #1 ✐ ✐ ✐ ✐ Math. Model. Nat. Phenom. Vol. 11, No. 2, 2016 …

Let Ω be a curvilinear polygon and Q Ω γ be the Laplacian in L 2 (Ω), Q Ω γ ψ=− Δ ψ, with the
Robin boundary condition∂ ν ψ= γ ψ, where∂ ν is the outer normal derivative and γ> 0. We …