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Xin Yang Lu CNA Title: Evolution schemes related to the average distance functional Abstract: The average distance problem was first introduced by Buttazzo, Oudet and Stepanov in [1], where the authors analyzed some properties of minimizing sets in two dimension domains. Many of these results were later extended by Paolini and Stepanov in [2] to higher dimension domains. Here we consider evolution schemes related to the average distance functional, and similarly to [1] and [2], we analyze geometric/analytic properties of solutions of such schemes.[1] Buttazzo G., Oudet E., Stepanov E., "Optimal transportation problems with free Dirichlet regions", Progr. in Nonlinear Diff. Eq. and App., vol. 51, pp. 41-65, 2002[2] Paolini E., Stepanov E., "Qualitative properties of maximum and average distance minimizers in $\mathbb{R}^n$", J. math. Sci.(N.Y.), 122(3), pp. 3290-3309, 2004 Recording (avi): http://mm.math.cmu.edu/recordings/cna/CNA-LuXinYang-Sep-25-2012.aviRecording (mp4): http://mm.math.cmu.edu/recordings/cna/CNA-LuXinYang-Sep-25-2012.mp4Date: Tuesday, September 25, 2012Time: 1:30 pmLocation: Wean Hall 7218Submitted by: David Kinderlehrer |