Smoothing for Nonlinear Parabolic Equations with Nonlinear Boundary Conditions

Of concern are parabolic problems of the form ­ ur­ ts= ? c x, =u. for x, t.gV=w0, T x with V;Rn, yc x, =u. ? n sb x, u. for x, t.g­V=w0, T x, u x, 0.sf x. for xgV. Under suitable conditions it is shown that for fgL1 V. and t ) 0, one has u ?, t. g L` V. and 5u ?, t.5` F C T. 5 f 51rt nr2 and 5ut ?, t.5 2FC T. 5 f 51rtnr4q1 for tg 0, T x and nG3. Analogous estimates are obtained with other powers of t in dimensions ns1, 2.