ESTIMATES ON THE (N-1)-DIMENSIONAL HAUSDORFF MEASURE OF THE BLOW-UP SET FOR A SEMILINEAR HEAT-EQUATION

We consider the following problem [GRAPHICS] where 1 < p < (N + 2)/(N - 2), and u0(x) is a continuous nonnegative and bounded function. It is shown here that for any blowing-up solution which is different from the uniform one u(T)(x,t) = ((p-1)(T-t))-1/(p-1) the (N-1)-dimensional Hausdorff measure of the blow-up set is bounded in compact sets of R(N).