Analysis Seminar
Speaker: Almut Burchard (Toronto)
"Symmetrization and sharp functional inequalities"
Time: 15:30
Room: MC 108
Symmetric decreasing rearrangement replaces
a given function $f$ on $\mathbb{R}^d$ by a radially decreasing
function $f^*$ that is equimeasurable to $f$. Symmetrization
techniques have been used to determine the sharp constants
in classical functional inequalities such as the Sobolev inequality, and for solving minimization problems in Geometry and Mathematical Physics. Symmetrization also
motivates the definition of rearrangement-invariant
function spaces.
I will describe recent work with A. Ferone
on the extremals of the Polya-Szego inequality.
The inequality says that the $p$-norms of the
gradient decrease under symmetrization. It is known
that there are non-trivial cases of equality, even
when $p>1$. We use Ryff's polar factorization to describe
these equality cases.
Speaker's homepage: http://www.math.toronto.edu/almut/
Mathematics Calendar 
Week of September 25, 2016
