2 citations · 2 across the 11 of their papers we have counts for
5 papers · 1 filter
Estimates on elliptic equations that hold only where the Hessian is large
Amit Kumar Acharya, Ram Baran Verma
In this article, we establish Hölder regularity for viscosity solutions to a class of degenerate fully nonlinear elliptic equations of the form \[ F(D^2u,Du)=f(x)~~\text{in}~~B_1,…
Liouville type theorems for fully nonlinear elliptic equations with superlinear growth in gradient
Amit Kumar Acharya, Ram Baran Verma
This article investigates positive supersolutions of the fully nonlinear elliptic system \[ \begin{cases} -\mathcal{M}_{λ,Λ}^{+}(D^{2}u)+|\nabla u|^{q} \geqλ_{1}f_{1}(v)~~\text{in}…
On the variational dual formulation of the Nash system and an adaptive convex gradient-flow approach to nonlinear PDEs
Dmitry Vorotnikov, Amit Acharya
We investigate the influence of base states on the consistency of the dual variational formulation for quadratic systems of PDEs, which are not necessarily conservative (typical ex…
Ideal Magnetohydrodynamics and Field Dislocation Mechanics
Amit Acharya
The fully nonlinear (geometric and material) system of Field Dislocation Mechanics is reviewed to establish an exact analogy with the equations of ideal magnetohydrodynamics (ideal…
A Hidden Convexity of Nonlinear Elasticity
Siddharth Singh, Janusz Ginster, Amit Acharya
A technique for developing convex dual variational principles for the governing PDE of nonlinear elastostatics and elastodynamics is presented. This allows the definition of notion…