INVERTING THE P-HARMONIC OPERATOR

The paper is concerned with the nonhomogeneous p-harmonic equation div \del u\(p-2) del u = div f. The main object is the operator H which c arries given vector function f into the gradient field del u. The natu ral domain of His the Lebesgue space L(q)(Omega, R(n)), where 1/p + 1/ q = 1. We extend the operator H to slightly larger spaces called grand L(q)-spaces. Continuity of H is used to prove existence and uniquenes s results for nonhomogeneous n-harmonic type equations div A(x, del u) = mu with mu a Radon measure.