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4:00 pm Thursday, October 8, 2009 Colloquium: Equilibrium solutions for variational problems with symmetryby Rafael de la Llave (University of Texas, Austin) in HB 227- We consider variational problems in media with periodic coefficients which satisfy some convexity properties. We will show that there are quasi-periodic solutions of all frequencies. We will also consider the problem of when there is a family of minimizers. The first example is the theory of Morse-Hedlund theory of geodesics on tori (and extensions by Ljusternik-Schnirelman). A later example the theory of Aubry-Mather (motivated by solid state physics and Lagrangian mechanics). An example of PDE's is homogenization theory. Families of minimizers corresponds to KAM theory.
Submitted by dani@rice.edu |