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We study the first order linear system Ui + iiw = 0, U w - iiz = ° in a domain n c C 2 (first considered by G. Cimmino, (3)). We prove a Morera type theorem, emphasizing the analogy to the Cauchy-Riemann system, and a representation formula yielding a result on removable singularities of solutions to (2). We derive (by a Hilbert space technique outlined in (5)) com­ patibility relations among the free terms and boundary data in the boundary value problem Ui + iiw = j, Ujii - iiz = g in n, and U = rp, v = tjJ on an. If F = (u, v) : n -t C2 is a solution to (2) such that sUPe>O SiJQ.IF(z, w)IP dae(z, w} < 00 for some p:2:: 2 then we show that F admits non tangential limits at almost every (C, CD) E an.

On first order linear PDE systems all of whose solutions are harmonic functions