A Priori Bounds for Global Solutions of Higher-order Semilinear Parabolic Problems

Abstract

In this paper, we derive a priori bounds for global solutions of 2m-th order semilinear parabolic equations with superlinear and subcritical growth conditions. The proof is obtained by a bootstrap argument and maximal regularity estimates. If n ≥ \frac{10}{3}m, we also give another proof which does not use maximal regularity estimates.