6 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}…
Shape Optimization for the Principal Eigenvalue of the Pucci Operator in Three Dimensions
Mohan Mallick, Ram Baran Verma
We investigate shape optimization for the principal eigenvalue of the Pucci extremal operator \[ \left\{ \begin{aligned} -\mathcal{M}^+_{λ,Λ}(D^{2}u)&=μ^{+}_{1}(Ω)u &&\text{in }Ω,\…
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, \end{c…
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,Λ}^+(D^2u…
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~~\tex…