On the Eigenvalues of the Biharmonic Steklov Problem on a Thin Set

ABSTRACT This paper investigates the asymptotic behavior of the eigenvalues of the biharmonic operator on a thin set with Steklov boundary conditions. The thin set is a tubular neighborhood of a planar smooth domain . We prove that, as , all Steklov eigenvalues satisfy , where is the th eigenvalue of an explicit one‐dimensional limiting problem on involving the curvature . The proof relies on the use of Fermi coordinates, a key coercivity estimate for the rescaled bilinear form, and ‐compact convergence of the associated resolvent operators.