12 citations · 44 across the 14 of their papers we have counts for
18 papers
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 t…
Gradient estimates for the Lagrangian mean curvature equation with critical and supercritical phase
Arunima Bhattacharya, Connor Mooney, Ravi Shankar
In this paper, we prove interior gradient estimates for the Lagrangian mean curvature equation, if the Lagrangian phase is critical and supercritical and . Combined with the…
Rigidity for general semiconvex entire solutions to the sigma-2 equation
Ravi Shankar, Yu Yuan
We show that every general semiconvex entire solution to the sigma-2 equation is a quadratic polynomial. A decade ago, this result was shown for almost convex solutions.
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…
Regularity for convex viscosity solutions of Lagrangian mean curvature equation
Arunima Bhattacharya, Ravi Shankar
We show that convex viscosity solutions of the Lagrangian mean curvature equation are regular if the Lagrangian phase has Hölder continuous second derivatives.
Regularity for convex viscosity solutions of special Lagrangian equation
Jingyi Chen, Ravi Shankar, Yu Yuan
We establish interior regularity for convex viscosity solutions of the special Lagrangian equation. Our result states that all such solutions are real analytic in the interior of t…
Hessian estimate for semiconvex solutions to the sigma-2 equation
Ravi Shankar, Yu Yuan
We derive a priori interior Hessian estimates for semiconvex solutions to the sigma-2 equation. An elusive Jacobi inequality, a transformation rule under the Legendre-Lewy transfor…
Recovering a quasilinear conductivity from boundary measurements
Ravi Shankar
We consider the inverse problem of recovering an isotropic quasilinear conductivity from the Dirichlet-to-Neumann map when the conductivity depends on the solution and its gradient…
Quasi-Noether systems and quasi-Lagrangians
V. Rosenhaus, Ravi Shankar
We study differential systems for which it is possible to establish a correspondence between symmetries and conservation laws based on Noether identity: quasi-Noether systems. We a…
Sub-symmetries II. Sub-symmetries and Conservation Laws
V Rosenhaus, Ravi Shankar
In our previous paper, the concept of sub-symmetry of a differential system was introduced, and its properties and some applications were studied. It was shown that sub-symmetries…
An inverse problem from condense matter physics
Ru-Yu Lai, Ravi Shankar, Daniel Spirn +1
We consider the problem of reconstructing the features of a weak anisotropic background potential by the trajectories of vortex dipoles in a nonlinear Gross-Pitaevskii equation. At…
Second Noether theorem for quasi-Noether systems
V. Rosenhaus, Ravi Shankar
Quasi-Noether differential systems are more general than variational systems and are quite common in mathematical physics. They include practically all differential systems of inte…
A strong maximum principle for nonlinear nonlocal diffusion equations
Ravi Shankar, Tucker Hartland
This is a study of a class of nonlocal nonlinear diffusion equations. We present a strong maximum principle for nonlocal time-dependent Dirichlet problems. Results are for bounded…
Symmetries and conservation laws of the Euler equations in Lagrangian coordinates
Ravi Shankar
We consider the Euler equations of incompressible inviscid fluid dynamics. We discuss a variational formulation of the governing equations in Lagrangian coordinates. We compute var…
Sub-symmetries I. Main properties and applications
V. Rosenhaus, Ravi Shankar
We introduce a sub-symmetry of a differential system as an infinitesimal transformation of a subset of the system that leaves the subset invariant on the solution set of the entire…
On a nonlocal extension of differentiation
Ravi Shankar
We study an integral equation that extends the problem of anti-differentiation. We formulate this equation by replacing the classical derivative with a known nonlocal operator simi…
Quantum simulations of a particle in one-dimensional potentials using NMR
Ravi Shankar, Swathi S. Hegde, T. S. Mahesh
A classical computer simulating Schrodinger dynamics of a quantum system requires resources which scale exponentially with the size of the system, and is regarded as inefficient fo…
Is the Model with the Hopf Term Exactly Equivalent to a Higher Spin Theory?
T. R. Govindarajan, R. Shankar, N. Shaji +1
We write down a local model involving two gauge fields, which is exactly equivalent to the O(3) model with the Hopf term. We impose the constraint by using the ga…