Regularity for Very Weak Solutions of A-Harmonic Equation with Weight.

This paper deals with very weak solutions of the A-harmonic equation divA(x,∇u) = 0 with the operator A : Ω × Rn → Rn satisfies some coercivity and controllable growth conditions with Muckenhoupt weight. By using the Hodge decomposition with weight, a regularity property is proved: There exists an integrable exponent r1 = r1(λ, n, p) < p, such that every very weak solution u ϵ Wloc1,r (Ω,w). That is, u is a weak solution to (✶) in the usual sense. [ABSTRACT FROM AUTHOR]