whereΩ is a bounded smooth domain ofRN ,N ≥ 1, with boundary ∂Ω,ai(u,v) are J-elliptic bilinear forms continuous on H1(Ω)×H1(Ω), (·,·) is the inner product in L2(Ω), and f i are J-regular functions. This system, introduced by Bensoussan and Lions (see [3]), arises in the management of energy production problems where J-units are involved (see [4] and the references therein). In the case studied...