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Sets of Anisotopic Minimal Boundary

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.

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