Frontiers in Mathematical Sciences
7th Conference University of Isfahan - January 1-3, 2020 |
Title:
Convex functional and the stratification of the singular set of
their stationary points
Speaker:
Zahra Sinaei, University of Massachusetts Amherst
Date, Time, and Venue: Wednesday, January 1 | 09:45-10:30 | Hall 2
Abstract:
In this talk, I discuss partial regularity of stationary
solutions and minimizers $u$ from a set $\Omega\subset \hspace{2pt}\mathbb{R}^n$ to a Riemannian
manifold $N$, for the functional $\int_\Omega F(x,u,|\nabla u|^2) dx.$ The
integrand $F$ is convex and satisfies some ellipticity, boundedness and
integrability assumptions. Using the idea of quantitative stratification I
show that the $k$-th strata of the singular set of such solutions are
$k$-rectifiable.
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