Higher integrability near the initial boundary for nonhomogeneous parabolic systems of p-Laplacian type

We establish a sharp higher integrability near the initial boundary for a weak solution to the following p-Laplacian type system: {u(t) - div A(x, t, del u) = div vertical bar F vertical bar(p-2) F + f in Omega(T), u = u(0) on Omega x {0}, by proving that, for given delta is an element of (0, 1), there exists epsilon > 0 depending on delta and the structural data such that vertical bar del(0)vertical bar(p+epsilon) is an element of L-loc(1)(Omega) and vertical bar F vertical bar(p+epsilon) vertical bar F vertical bar((delta p(n+2)/n)')+epsilon is an element of L-1(0, T; L-loc(1 )(Omega)) double right arrow vertical bar del u vertical bar(p+epsilon) is an element of L-1 (0, T; L-loc(1) (Omega)). Our regularity results complement established higher regularity theories near the initial boundary for such a nonhomogeneous problem with f not equal 0 and we provide an optimal regularity theory in the literature.