exterior domain 1fully nonlinear elliptic equations 1gradient superlinear growth 1liouville theorems 1nonexistence results 1pucci operator 1
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math.AP2026
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,…
math.AP2026
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…
math.AP2025
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…