From the 1 of 10 linked papers with an AI index.
10 papers
Solving the Dissipation Inequality not as a constitutive restriction
Maximiliano Larrain Silva, Amit Acharya
A solution procedure is formulated and solved for treating the nonlinear Dissipation Inequality as a constraint equation within continuum mechanics, and allowing for incomplete kno…
Dual Variational Principles for Curl Forces
Arash Yavari, Amit Acharya
Curl forces are position-dependent, non-conservative, and non-dissipative forces that, in general, cannot be derived from an ordinary potential energy. Consequently, their equation…
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
The paper proves sharp Liouville‑type nonexistence results for positive supersolutions of fully nonlinear elliptic systems with superlinear gradient terms, using the extremal Pucci…
Hamilton-Jacobi as model reduction, extension to Newtonian particle mechanics, and a wave mechanical curiosity
Amit Acharya
The Hamilton-Jacobi equation of classical mechanics is approached as a model reduction of conservative particle mechanics where the velocity degrees-of-freedom are eliminated. This…
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…