Research Group:
Speaker:
Shokhrukh Kholmatov
Institution:
SISSA
Schedule:
Friday, January 15, 2016 - 14:00
Location:
A-133
Abstract:
I would like to discuss about local minimizers of anisotropic (or weighted) area functional $\int_{M} F(n) H^{n-1}$ on $R^n$, where $M$ is a boundary of a set of locally finite perimeter, $n$ is the unit normal to its reduced boundary, $H^m$ is the $m$-dimensional Hausdorff measure, and F is an anisotropy. For the isotropic case (i.e., when F is the euclidean norm) many remarkable regularity and classification results were obtained during the past 50 years. Interesting questions would be the following: what results still hold for anisotropic case? What kind of results which are absent in isotropic case can be expected? I would like to talk about answers to these questions.
This is joint work with G. Bellettini and M. Novaga.