A note on the a.e. second-order differentiability of rank-one convex functions

In the Euclidean setting, the well-known Alexandrov theorem states that convex functions are twice differentiable almost everywhere.

In this talk, the theorem is extended to rank-one convex functions. The approach is novel in that it draws more from viscosity techniques developed in the context of fully nonlinear elliptic equations.

As a byproduct, the original Alexandrov theorem can essentially be reduced to the a.e. differentiability of one-dimensional monotone functions, which will be presented if time permits.