Bulk-Boundary Eigenvalues for Bilaplacian Problems

The paper defines the bulk–boundary bilaplacian eigenproblem via the Rayleigh quotient E_γ and the space H^2_*(Ω), proves monotonicity, continuity in γ ∈ [0,∞], and the limits as γ→0 and γ→∞ (with the Steklov-type limit and eigenfunction rescaling), see the functional setup and min–max characterization (2.1)–(2.8) and Theorem 3.3 . The candidate solution establishes exactly these facts using a variational compactness approach, a norm-equivalence on H^2_*(Ω), and a trace–Poincaré inequality to control the γ→∞ regime, ultimately identifying the Steklov limit and eigenfunction convergence. While the paper streamlines the γ→∞ passage by reparameterizing t=γ^{-1} and appealing to the same min–max continuity scheme, the model gives a more granular argument using boundary orthogonality and Courant–Fischer. No substantive conflicts were found; the proofs are methodologically different but mathematically consistent with the paper’s results, including the limiting Steklov problem (2.11) and the compact embedding H^2_*(Ω)↪L^2_γ(Ω,∂Ω) .