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math.AP2024
Hessian estimates for the sigma-2 equation in dimension four
Ravi Shankar, Yu Yuan
We derive a priori interior Hessian estimates and interior regularity for the equation in dimension four. Our method provides respectively a new proof for the corresponding…
math.AP2024
Optimal regularity for Lagrangian mean curvature type equations
Arunima Bhattacharya, Ravi Shankar
We classify regularity for Lagrangian mean curvature type equations, which include the potential equation for prescribed Lagrangian mean curvature and those for Lagrangian mean cur…