Local Calderon-Zygmund estimates for parabolic minimizers

We establish local Calderon-Zygmund estimates for parabolic minimizers u to certain variational inequalities. The formal corresponding parabolic partial differential equation would be partial derivative(t)u - div partial derivative(zeta)f(z, u, Du) = -partial derivative(u)f(z, u, Du) + div(vertical bar F vertical bar Fp-2) + h, with p >= 2n/(n + 2). However, since we do not impose any condition on the existence of the derivative partial derivative(u)f, the PDE above may not have any meaning at all. For proving the Calderon-Zygmund estimates, we thus remain solely on the level of parabolic minimizers. Precisely, for q > p we prove that Du is an element of L-loc(q) if u is locally Holder continuous and F is an element of L-loc(q) and h is an element of L-loc(Q) for a Q depending on q. (C) 2015 Elsevier Ltd. All rights reserved.