HIGHER INTEGRABILITY FOR PARABOLIC SYSTEMS WITH NON-STANDARD GROWTH AND DEGENERATE DIFFUSIONS

The aim of this paper is to establish a Meyer's type higher integrability result for weak solutions of possibly degenerate parabolic systems of the type partial derivative(t)u - div a(x, t, Du) = div(vertical bar F vertical bar F-p(x,F- t)-2). The vector-field a is assumed to fulfill a non-standard p(x, t)-growth condition. In particular it is shown that there exists epsilon > 0 depending only on the structural data such that there holds: vertical bar Du vertical bar(p(.)(1+epsilon)) is an element of L-loc(1), together with a local estimate for the p(.)(1+epsilon)-energy.