We study localization properties of low-lying eigenfunctions of magnetic Schrödinger
operators (− i∇− A (x)) 2 ϕ+ V (x) ϕ= λ ϕ, where V: Ω→ R≥ 0 is a given potential and A: Ω→ …

Abstract Let Ω⊂ R 2 be a bounded, convex domain and let− Δ ϕ 1= μ 1 ϕ 1 be the first
nontrivial Laplacian eigenfunction with Neumann boundary conditions. The hot spots …

Abstract The Hermite–Hadamard inequality states that the average value of a convex
function on an interval is bounded from above by the average value of the function at the …

We study directed, weighted graphs G=(V, E) and consider the (not necessarily symmetric)
averaging operator (L u)(i)=−∑ j∼ ipij (u (j)− u (i)), where pij are normalized edge weights …

We discuss explicit landscape functions for quantum graphs. By a “landscape function”
$\Upsilon (x) $ we mean a function that controls the localization properties of normalized …

We derive a lower bound on the location of global extrema of eigenfunctions for a large
class of non-local Schrödinger operators in convex domains under Dirichlet exterior …

For an open set\(\Omega\subset\mathbb {R}^ 2\) let\(\lambda (\Omega)\) denote the bottom
of the spectrum of the Dirichlet Laplacian acting in\(L^ 2 (\Omega)\). Let\(w_\Omega\) be the …

We study localization properties of low-lying eigenfunctions (− Δ+ V) ϕ= λ ϕ in Ω for rapidly
varying potentials V in bounded domains Ω⊂ R d. Filoche & Mayboroda introduced the …

Abstract Let Ω ⊂ R^ 2 Ω⊂ R 2 be a bounded, convex domain and let u be the solution of-Δ
u= 1-Δ u= 1 vanishing on the boundary ∂ Ω∂ Ω. The estimate ‖ ∇ u ‖ _ L^ ∞ (Ω) ≤ c …

Let⊂ Rn be a bounded domain satisfying a Hayman-type asymmetry condition, and let D be
an arbitrary bounded domain referred to as an “obstacle”. We are interested in the behavior …