... c, with φ ∈ [Lp(Σ)]2, c ∈ R2. In all other cases, ψ can be written as (55) with φ ∈ [Lp(Σ)]n. In any case, sincedψ = Rφ (R being defined by (23)), we infer R(dψ) = RRφ. Keeping in ... potential. This leads to the construction of a reducing operator, which will be useful in the study of the integral system of the first kind arising in theDirichlet problem.Section 4 is devoted ... [Lp(Σ)]nsolves the singular integral system Rϕ = df with R as in (23).Proof. Consider the following singular integral system:Σdx[Γ(x, y)] ϕ(y) dσy= df(x), x ∈ Σ, (45) in which the unknown...