Center for                           Nonlinear Analysis CNA Home People Seminars Publications Workshops and Conferences CNA Working Groups CNA Comments Form Summer Schools Summer Undergraduate Institute PIRE Cooperation Graduate Topics Courses SIAM Chapter Seminar Positions Contact CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium Timothy Blass Center for Nonlinear Analysis, Carnegie Mellon University Title: Aubry-Mather theory for PDEs Abstract: I will discuss the Aubry-Mather theory for PDEs, where one is interested in constructing plane-like minimizers of (formal) energy functionals on $\mathbb{R}^n$ with some periodicity assumptions. First, we solve the case where the average slope of the minimizer is rational, which has an associated cell problem. By taking limits of the rational case, we can then construct plane-like solutions with irrational average slope. I will present a gradient descent approach to constructing these plane-like minimizers as well as a perturbation theory approach in the case that the energy is a perturbation of an "integrable" energy(note: if 7218 is still in use, we go to 8220)Recording: http://vnc.math.cmu.edu/cna/CNA-Blass-Oct-04-2011.aviRecording: http://vnc.math.cmu.edu/cna/CNA-Blass-Oct-04-2011.mp4Pdf File: TimBlass.pdfDate: Tuesday, October 4, 2011Time: 1:30 pmLocation: Wean Hall 7218Submitted by:  David Kinderlehrer