Nicola Fusco, Dip. Mat. Univ. Napoli
"Polya-Szego type inequalities for Steiner symmetrization: cases of equality"
The classical Polya-Szego inequality says that if is a nonnegative smooth
function with compact support and is its
Steiner symmetral, then
for all . In particular, when is the characteristic function of a set of finite perimeter, the previous inequality implies that where denotes the perimeter of and is the Steiner symmetral of with respect to a given hyperplane.
We shall discuss what can be said about the case of equality holds in the two previous inequalities.
TUESDAY, February 24, 2004