SMOOTHING FOR NONLINEAR PARABOLIC EQUATIONS WITH NONLINEAR BOUNDARY-CONDITIONS

Of concern are parabolic problems of the form partial derivative u/par tial derivative t = del.psi(x, del u) for (x, t) is an element of Omeg a x [0, T] with Omega subset of R-n, -psi(x, del u).nu = beta(x, u) fo r (x, t) is an element of partial derivative Omega x [0, T], u(x, 0) = f(x) for x is an element of Omega. Under suitable conditions it is sh own that for f is an element of L-1(Omega) and t > 0, one has u(., t) is an element of L-infinity(Omega) and \\u(., t)\\(infinity) less than or equal to C(T) \\f\\(1)/t(n/2) and \\u(t)(., t)\\(2) less than or e qual to C(T)\\f\\(1)/tn/4 + 1 for t is an element of (0, T] and n grea ter than or equal to 3. Analogous estimates are obtained with other po wers of t in dimensions n = 1, 2. (C) 1997 Academic Press.