4 papers
Counterexamples to maximal regularity for operators in divergence form
Sebastian Bechtel, Connor Mooney, Mark Veraar
In this paper, we present counterexamples to maximal -regularity for a parabolic PDE. The example is a second-order operator in divergence form with space and time-dependent c…
Semi-convex viscosity solutions of the special Lagrangian equation
Connor Mooney, Ravi Shankar
We prove smoothness and interior derivative estimates for viscosity solutions to the special Lagrangian equation with almost negative phases and small enough semi-convexity. We sho…
Remarks on the quadratic Hessian equation
Connor Mooney
We prove that viscosity solutions to the quadratic Hessian equation cannot touch a harmonic function on a minimal surface from below. This can be viewed as a for…
Solutions to the minimal surface system with large singular sets
Connor Mooney, Ovidiu Savin
Lawson and Osserman proved that the Dirichlet problem for the minimal surface system is not always solvable in the class of Lipschitz maps. However, it is known that minimizing seq…