51 citations · 52 across the 7 of their papers we have counts for
5 papers · 1 filter
Doubling and the two-dimensional critical valued Lagrangian phase
Arunima Bhattacharya, Ravi Shankar, Jeremy Wall
In this paper, we establish interior Hessian and gradient estimates for the two-dimensional Lagrangian mean curvature equation when the phase changes signs, provided the gradient o…
Singularities of the Lagrangian mean curvature flow at the critical Lagrangian phase
Arunima Bhattacharya, Ravi Shankar, Jeremy Wall +1
We establish interior estimates for singularities of the Lagrangian mean curvature flow when the Lagrangian phase is critical, i.e., , and extend our resul…
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…
Removing singularities for fully nonlinear PDEs
Ravi Shankar
We show removability of half-line singularities for viscosity solutions of fully nonlinear elliptic PDEs which have classical density and a Jacobi inequality. An example of such a…
Hessian estimates for special Lagrangian equation by doubling
Ravi Shankar
New, doubling proofs are given for the interior Hessian estimates of the special Lagrangian equation. These estimates were originally shown by Chen-Warren-Yuan in CPAM 2009 and Wan…