A PRIORI BOUNDS FOR GLOBAL SOLUTIONS OF HIGHER-ORDER SEMILINEAR PARABOLIC PROBLEMS

摘要

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