Carnegie Mellon
Department of Mathematical 

Nicola Fusco, Dip. Mat. Univ. Napoli

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


The classical Polya-Szego inequality says that if $u$ is a nonnegative smooth function with compact support and $u^s$ is its Steiner symmetral, then

\int\vert\nabla u\vert^p\,dx\geq\int\vert\nabla u^s\vert^p\,dx

for all $p>1$. In particular, when $u$ is the characteristic function of a set $E$ of finite perimeter, the previous inequality implies that $ P(E)\geq P(E^s) \,, $ where $P(E)$ denotes the perimeter of $E$ and $E^s$ is the Steiner symmetral of $E$ 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