The paper is concerned with the nonhomogeneous p-harmonic equation div |▽u|p-2▽u = div f . The main object is the operator H which carries given vector function f into the gradient field ▽u. The natural domain of H is the Lebesgue space Lq(Ω, ℝn), where 1/p + 1/q = 1. We extend the operator H to slightly larger spaces called grand Lq-spaces. Continuity of H is used to prove existence and uniqueness results for nonhomogeneous n-harmonic type equations div A(x, Vu) = μ with μ a Radon measure.
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