VERY WEAK SOLUTIONS OF HIGHER-ORDER DEGENERATE PARABOLIC SYSTEMS

We consider non-linear higher-order parabolic systems whose simplest model is the parabolic p-Laplacean system integral(Omega T) u . phi(t) - <vertical bar D(m)u vertical bar(p-2) D(m)u, D(m)phi > dz = 0 It turns out that the usual regularity assumptions on solutions can be weakened in the sense that going slightly below the natural integrability exponent still yields a classical weak solution. Namely, we prove the existence of some beta > 0 such that D(m)u is an element of L(p-beta) double right arrow D(m)u is an element of L(p+beta).