From the 2 of 6 linked papers with an AI index.
6 papers
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…
Shape Optimization for the Principal Eigenvalue of the Pucci Operator in Three Dimensions
Mohan Mallick, Ram Baran Verma
The paper studies how the shape of a three‑dimensional domain affects the principal eigenvalue of the fully nonlinear Pucci extremal operator, showing that a symmetric, unsheared d…
Lane--Emden Systems with Singular Nonlinearities for the Fully Nonlinear Elliptic Operator
Karan Rathore, Mohan Mallick, Ram Baran Verma
Consider \[ \begin{cases} F(D^2 u,Du,u,x) = u^{-p}v^{-q},~\text{in}~Ω\\ F(D^2 v,Dv,v,x)=u^{-r}v^{-s},~~\text{in}~~Ω\\ u,v>0~~\text{in}~~Ω\\ u=v=0~\quad~\text{on}~~\partialΩ, \e…
Exceptional Boundary Sets for Solutions of Fully Nonlinear Parabolic PDEs
Ram Baran Verma, Mohan Mallick
This article investigates the exceptional set of the boundary for the following problem: \begin{equation*} \begin{aligned} -\frac{\partial u}{\partial t} + \mathcal{M}_{λ,Î}^+(D^…
Regularity for Fully Nonlinear Elliptic Equations with Natural Growth in Gradient and Singular Nonlinearity
Mohan Mallick, Ram Baran Verma
In this article we consider the following boundary value problem \begin{equation*}\label{abs} \left\{ \begin{aligned} F(x,u,Du,D^{2}u)+c(x)u+ p(x)u^{-α}&=0~\text{in}~Ω\\ u&=0~~\t…