Hölder continuity of solutions for higher order degenerate nonlinear parabolic equations (Q1570173)

The authors consider a nonlinear differential equation of parabolic type with hypotheses on the coefficients to be Caratheodory's functions. The aim of this note is to prove interior regularity of an arbitrary bounded solution of the parabolic equation. Boundedness of solutions for equations of the same type is obtained in a previous paper of the authors to appear in Commun. Partial Differ. Equ. entitled ``On existence and boundedness of solution for degenerate quasilinear parabolic equations of higher type''. The method used by Nicolosi and Skrypnik to obtain useful integral inequalities is based on estimates for weighted functions and then on Hölder and Young inequalities. Let us point out that in the last section the authors give an example of weighted functions that satisfy the assumptions requested and establish their result in a general form.