Author

Ram Baran Verma

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Preprint Oct 2026

Weighted Liouville Theorems and A Priori Bounds for Indefinite Superlinear Equations with Pucci's Maximal Operator

Consider \begin{equation*}\ \left\{ \begin{aligned} -\mathcal_{\lambda,\Lambda}^{+}(D^{2}u)&=\mu u+a(x)u^{p}\quad\text{in}~\Omega,\\ u&=0\quad\text{on}~~\partial\Omega, \end{aligned} \right. \end{equation*} where $ \ Omega$ is a smooth bounded domain, $a$ is a continuous function which is allowed to change sign. Moreov...

Karan Rathore, Mohan Mallick, Ram Baran Verma · 0 citations

Preprint Jul 2026

Estimates on elliptic equations that hold only where the Hessian is large

In this article, we establish H\"older regularity for viscosity solutions to a class of degenerate fully nonlinear elliptic equations of the form \[ F(D^2u,Du)=f(x)~~\text{in}~~B_1, \] where the operator is elliptic only in regions where the Hessian is sufficiently large. Such equations arise naturally in free boundary...

Amit Acharya, Ram Baran Verma · 0 citations