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We are concerned with the possibility of identifying the real parameters a and b on the right-hand side of the equation u = au + b 0 inω R 2 (0.1) for a function u satisfying the boundary conditions u = 0, ∂u/∂ν = on ∂ω (0.2) with any fixed sufficiently smooth function ≡ 0.In the case of a smooth curve γ = ∂ω, we provide a sufficient condition, under which the pair (a, b) can be uniquely reconstructed through the specified function . On the basis of this sufficient condition, we show that there are at most finitely many pairs (a, b) if ω is (simply connected and) different from a disc.If ω has a corner we prove that the pair (a, b) is unique and can be calculated explicitly if is known on one side near the corner.

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