5 papers
Twice differentiability of solutions to fully nonlinear parabolic equations near the boundary
Karthik Adimurthi, Agnid Banerjee, Ram Baran Verma
In this paper, we prove regularity for viscosity solutions to non-convex fully nonlinear parabolic equations near the boundary. This constitutes the parabolic c…
Borderline gradient estimates at the boundary in Carnot groups
Ramesh Manna, Ram Baran Verma
In this article, we prove the continuity of the horizontal gradient near a non-characteristic portion of the boundary for solutions to pert…
Regularity for degenerate fully nonlinear elliptic equations with Neumann boundary conditions
Agnid Banerjee, Ram Baran Verma
In this paper, we establish regularity upto the boundary for a class of degenerate fully nonlinear elliptic equations with Neumann boundary conditions. Our main result T…
Lyapunov type inequality for extremal Pucci's equations
J. Tyagi, R. B. Verma
In this article, we establish Lyapunov type inequality for the following extremal Pucci's equation \begin{equation*} \left\{ \begin{aligned}{} \mathcal{M}^{+}_{λ,Λ}(D^{2}u)+a(x)u&=…
On the bifurcation for fractional Laplace equations
Gaurav Dwivedi, Jagmohan Tyagi, Ram Baran Verma
In this paper, we consider the bifurcation problem for fractional Laplace equation \begin{eqnarray*} \begin{array}{ll} (-Δ)^{s} u = λu + f(λ,\,x,\,u)& \mbox{in }Ω, u = 0 &\mbox{in…