In this talk, we study the regularity properties of the solutions to degenerate elliptic equations and non-strictly convex minimization problems. Generally, the solutions are not continuously differentiable. Therefore, we are studying a particular function of the gradient: the stress-field. First, we present two results stated in dimension two and their proofs. The second part is dedicated to a result in higher dimension. Finally, we will see some applications and open questions related to the aforementioned results.
Camille Labourie