The norm and the essential norm of the double layer elastic and hydrodynamic potentials in the space of continuous functions

We study a class of matrix integral operators which appear as limit values of the double layer potentials. We find general representations for the norms and for the essential norms of such operators in the space of continuous vector‐valued functions. These representations are specified for boundary integral operators of linear isotropic elasticity theory and hydrodynamics of viscous incompressible fluid under the assumption that there is an angle point on the boundary of a plane domain and a conic point or an edge on the boundary of a three‐dimensional domain.