Symmetry in rearrangement optimization problems.
We consider the -Laplacian operator on a domain equipped with a Finsler metric. We recall relevant properties of its first eigenfunction for finite and investigate the limit problem as .
Small amplitude vibrations of an elastic structure completely filled by a fluid are considered. Describing the structure by displacements and the fluid by its pressure field one arrives at a non-selfadjoint eigenvalue problem. Taking advantage of a Rayleigh functional we prove that its eigenvalues can be characterized by variational principles of Rayleigh, minmax and maxmin type.