Abstract:
In this talk, we shall discuss our recent work which shows that in the periodic homogenization of viscous HJ equations in any spatial dimension the effective Hamiltonian does not necessarily inherit the quasiconvexity property (in the momentum variables) of the original Hamiltonian. Moreover, the loss of quasiconvexity is, in a way, generic: when the spatial dimension is 1, every convex function can be modified on an arbitrarily small interval so that the modified function, G(p), is quasiconvex, and for some Lipschitz continuous periodic V(x), the effective Hamiltonian corresponding to H(p,x)=G(p)+V(x) is not quasiconvex. This observation is in sharp contrast with the inviscid case where homogenization preserves quasiconvexity. The talk is based on joint work with Atilla Yilmaz, Temple University.
Biography:
Elena Kosygina is a Visiting Professor of Mathematics at NYU Shanghai and a Professor of Mathematics at Baruch College and the CUNY Graduate Center. After completing her PhD at the Courant Institute of Mathematical Sciences, NYU, she was a (non-tenure-track) R. Boas Assistant Professor at Northwestern University, and then moved to CUNY to a tenure-track position and received tenure. She was a member of the Institute of Advanced Studies (Spring 2009) and a Simons Fellow in Mathematics (2014-2015). Prof. Kosygina's research is in probability, stochastic processes, and partial differential equations. In particular, she is interested in scaling limits of self-interacting random walks and in homogenization of Hamilton-Jacobi equations in random media.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai
This event is open to the NYU Shanghai community and Math community.