Singularities of elliptic mixed boundary problems. Application to boundary stabilization of hyperbolic systems

For elliptic partial differential equations, mixed boundary conditions generate singularities in the solution, mainly when the boundary of the domain is connected. We here consider two classical cases: the Laplace equation and the Lamé system. The knowledge of singularities allows us to construct adapted Rellich relations. These are useful in the problem of boundary stabilization of the wave equation and the elastodynamic system, respectively, when using the multiplier method.