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In this paper we deal with the stationary Navier-Stokes problem in a domain with compact Lipschitz boundary ∂ and datum a in Lebesgue spaces. We prove existence of a solution for arbitrary values of the fluxes through the connected components of ∂ , with possible countable exceptional set, provided a is the sum of the gradient of a harmonic function and a sufficiently small field, with zero total flux for bounded.

The traction problem for the Stokes system is studied in the framework of the theory of the hydrodynamical potentials. Existence theorems and integral representations of classical solutions are given for domains having not connected boundary of class C1,α in both the bounded and exterior cases. Finally, a maximum modulus theorem is derived for the traction field in the direction of the normal to the boundary.

We deal with the system of equations of linear elastostatics, governing the equilibrium configurations of a linearly elastic body. We recall the basics of the theory of the elastic layer potentials and we extend the trace operators associated with the layer potentials to suitable sets of singular densities. We prove that the trace operators defined, for example, on W 1 − k − 1 / q , q ( ∂ Ω ) (with k ≥ 2 , q ∈ ( 1 , + ∞ ) and Ω an open connected set of R 3 of class C k ), satisfy the Fredholm property.

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