Oberseminar Analysis Summer 2014

Organizers: B. Zwicknagl, S. Conti, H. Koch, S. Müller, B. Niethammer, M. Rumpf, C. Thiele, J. López-Velázquez

  • Thursday, April 10, 2:15 pm, seminar room 0.011
    Riccardo Adami (Politecnico di Torino)
    Miniminzing NLS energy on graphs
    Owing to the loss of translational symmetry, the Nonlinear Schroedinger Equation on star graphs consisting of at least two infinite edges shows the lack of ground states. In this talk it will be shown how to extend this result to a more general class of graphs with Kirchhoff's (i.e. free) conditions at vertices, and an example will be given in which, on the other hand, the ground state exists.
    This is a joint work in progress with E. Serra and P. Tilli (Politecnico di Torino).


  • Thursday, May 8, 2:15 pm, Lipschitz-Saal
    Paolo Tilli (Politecnico di Torino)
    A minimization approach to hyperbolic Cauchy problems
    We will discuss some recent results obtained in
    collaboration with E. Serra, concerning a minimization
    approach to a wide family of hyperbolic Cauchy problems.
    This general and abstract approach, that stems from a
    conjecture of De Giorgi in a particular case, allows the approximation of
    solutions to Cauchy problems by functions that minimize
    suitable functionals in space-time. Also equations
    with dissipative terms can be treated. Focus will be on
    recent results and some related open questions.


  • Thursday, June 26, 2:15 pm, Lipschitz-Saal
    Peter Gladbach
    A twice-relaxed sharp-interface limit in multiple slip-plane plasticity.
    We study a continuum model for plastic slips in multiple parallel slip planes embedded into an elastic crystal. This model contains two length scales, the lattice parameter and the distance of the planes.
    Generalizing a result by S. Conti, A. Garroni, and S.Mueller, we obtain a sharp-interface limit energy, penalizing edge dislocations.
    Depending on the scaling law of the two length scales, the limit line-tension energy may feature an iterative relaxation behavior and induce microstructure at multiple length scales.
    We shall outline the basic steps in proving an upper and a lower bound.


  • Thursday, July 10, 2:15 pm, seminar room 2.040
    Nicholas Alikakos (University of Athens)
    On the structure of phase transition maps: density estimates and applications
    The scalar Allen-Cahn ( or Ginzburg- Landau ) equation is
    related to Minimal Surfaces and Minimal Graphs via the level sets of its
    solutions.  The Vector Allen-Cahn is related to Plateau Complexes. These
    are non-orientable minimal objects with a hierarchical structure. After
    explaining these relationships we focus on vector extensions of the
    Caffarelli-Cordoba  Density Estimates (L. Caffarelli and A.Cordoba , Comm.
    Pure and Applied Mathematics Volume 48, Issue 1, pages 1–12, January 1995).
    In particular we establish lower co-dimension density estimates. These
    are useful for studying the hierarchical structure of certain entire
    vector solutions. We also give applications to minimal solutions (lower
    bounds, Liouville theorems)

    Joint work with: Giorgio Fusco

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