Convex integration techniques have been used to produce solutions with precise regularity, which are necessary for the resolution of the Onsager conjecture for the 3D Euler equations, or solutions ...

A new nonparametric estimate of a convex regression function is proposed and its stochastic properties are studied. The method starts with an unconstrained estimate of the derivative of the regression ...

We discuss first-order systems of nonlinear conservation laws which have as a consequence an additional conservation law. We show that if the additional conserved quantity is a convex function of the ...

These functions, which are characterised by their upper semi-continuity and subharmonicity along complex lines, are instrumental in formulating and solving complex Monge-Ampère equations.