The Poisson problem for the Lamé system on low dimensional Lipschitz domains

where ν is the unit normal to ∂Ω and the superscript t indicates transposition (in this case, of the matrix ∇~u = (∂ju)j,α). Relying on the method of layer potentials and suitable Rellich-NečasPayne-Weinberger formulas, the boundary value problems (1.2)-(1.3) with ~ f = 0 and ~g ∈ L(∂Ω), 2− ε < p < 2 + ε, have been treated (in all spacedimensions) by B. Dahlberg, C.Kenig, and G.Verchota (cf. [7]). In the three-dimensional setting, these results have been subsequently extended to optimal ranges of p’s (2−ε < p ≤ ∞ for the Dirichlet boundary condition, and 1 < p < 2+ε for the traction boundary condition, with ε = ε(∂Ω) > 0) in [6]. More recently, the results for the Dirichlet problem (i.e., (1.2) with