4 papers
A note on relations between convexity and concavity of thermodynamic functions
Mária Lukáčová-Medvid'ová, Ferdinand Thein, Gerald Warnecke +1
The paper is concerned with proving the equivalence of convexity or concavity properties of thermodynamic functions, such as energy and entropy, depending on different sets of vari…
Quadratic Hessian equation
Yu Yuan
We survey quadratic Hessian equations: definition, background, rigidity of entire solutions, regularity of viscosity solutions, a priori Hessian estimates, and open problems.
A constant rank theorem for special Lagrangian equations
W. Jacob Ogden, Yu Yuan
Constant rank theorems are obtained for saddle solutions to the special Lagrangian equation and the quadratic Hessian equation. The argument also leads to Liouville type results fo…
Regularity for the Monge-Ampère equation by doubling
Ravi Shankar, Yu Yuan
We give a new proof for the interior regularity of strictly convex solutions of the Monge-Ampère equation. Our approach uses a doubling inequality for the Hessian in terms of the e…