Frequency functions, monotonicity formulas, and the thin obstacle<br/><br/>problem

Monotonicity formulas play a pervasive role in the study of
variational inequalities and free boundary problems. In this talk we will
describe a new approach to a classical problem, namely the thin obstacle (or
Signorini) problem, based on monotonicity properties for a family of
so-called frequency functions.

Donatella Danielli is a Professor of Mathematics at Purdue
University. She received a Laurea cum Laude in Mathematics from the
University of Bologna, Italy (1989), and a Ph.D. degree in Mathematics from
Purdue University (1999) under the direction of Carlos Kenig. Her research
areas are partial differential equations, harmonic analysis, and
sub-Riemannian geometry. She has been the recipient of an NSF CAREER Award,
a Purdue University Teaching for Tomorrow Award, and a Ruth and Joel Spira
Award for Graduate Teaching. Before joining the Purdue University faculty in
2001, she held positions at The Johns Hopkins University and at the Institut
Mittag-Leffler in Sweden. She is the author of 40 published papers and 2
monographs. She is the creator and organizer of the Symposia on Analysis and
PDEs and the Women in Mathematics Days, both at Purdue University.