Center for                           Nonlinear Analysis CNA Home People Seminars Publications Workshops and Conferences CNA Working Groups Summer Schools Summer Undergraduate Institute PIRE Cooperation Graduate Topics Courses SIAM Chapter Seminar Positions Contact CNA Seminar 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