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# Cyrill Muratov : On shape of charged drops: an isoperimetric problem with a competing non-local term

In this talk I will give an overview of my recent work with H. Knuepfer on the analysis of a class of geometric problems in the calculus of variations. I will discuss the basic questions of existence and non-existence of energy minimizers for the isoperimetric problem with a competing non-local term. A complete answer will be given for the case of slowly decaying kernels in two space dimensions, and qualitative properties of the minimizers will be established for general Riesz kernels.

**Category**: Applied Math and Analysis**Duration**: 01:34:55**Date**: February 25, 2013 at 4:25 PM**Views**: 130-
**Tags:**seminar, Applied Math And Analysis Seminar

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