Symmetrization in parabolic neumann problems
Marco Bramanti · Applicable Analysis · 1991
We consider the Cauchy-Neumann problem for parabolic operators of the kind: on a smooth cylinder [0,T]×Ω. By symmetrization techniques we establish for the solution u of this problem an estimate of the kind: where U is the solution of a symmetrized problem and u(t)*(·) is the decreasing rearrangement of u(t,.). We also obtain an “energy inequality” comparing norms of the gradients of u and U