Some properties of Bessel functions with applications to Neumann eigenvalues in the unit disc

Sammanfattning: A study is made of the multiplicities of the eigenvalues of the Laplace operator in the unit disc with Neumann boundary conditions. Our result is that all eigenvalues are simple or double, a result which is well-known if one instead considers Dirichlet boundary conditions. The result is proved by using some properties of Bessel functions. We also give an application to standing water waves in a cylinder.