## Nicola Fusco, Dip. Mat. Univ. Napoli

"Polya-Szego type inequalities for Steiner symmetrization: cases of equality"

#### Abstract

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
Time: 1:30 P.M.
Location: PPB 300