On the eigenvalues of the biharmonic operator with Neumann boundary conditions on a thin set
Francesco Ferraresso, Luigi Provenzano · Bulletin of the London Mathematical Society · 2023
Abstract Let be a bounded domain in with smooth boundary , and let be the set of points in whose distance from the boundary is smaller than . We prove that the eigenvalues of the biharmonic operator on with Neumann boundary conditions converge to the eigenvalues of a limiting problem in the form of a system of differential equations on .