3 citations · 6 across the 6 of their papers we have counts for
8 papers
Improved Hardy inequalities on Riemannian Manifolds
Kaushik Mohanta, Jagmohan Tyagi
We study the following version of Hardy-type inequality on a domain in a Riemannian manifold : $$ \intΩ|\nabla u|_g^pρ^αdV_g \geq \left(\frac{|p-1+β|}{p}\right)^p\intΩ\f…
Regularity of solutions to variable-exponent degenerate mixed fully nonlinear local and nonlocal equations
Priyank Oza, Jagmohan Tyagi
We consider a class of variable-exponent mixed fully nonlinear local and nonlocal degenerate elliptic equations, which degenerate along the set of critical points, $C:=\big\{x:\,Du…
The Neumann problem for a class of semilinear fractional equations with critical exponent
Somnath Gandal, Jagmohan Tyagi
We establish the existence of solutions to the following semilinear Neumann problem for fractional Laplacian and critical exponent: \begin{align*}\left\{\begin{array}{l l} { (-Δ)^{…
Mixed fully nonlinear local and nonlocal elliptic operators in Heisenberg group
Priyank Oza, Jagmohan Tyagi
We establish the comparison principle, existence and regularity of viscosity solutions to the following problem concerning the mixed operator: \begin{align} \begin{cases} α\mathcal…
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…
Singular Adams inequality for biharmonic operator on Heisenberg Group and its applications
Gaurav Dwivedi, Jagmohan Tyagi
The goal of this paper is to establish singular Adams type inequality for biharmonic operator on Heisenberg group. As an application, we establish the existence of a solution to \b…
Stability of positive solutions to biharmonic equations on Heisenberg group
Gaurav Dwivedi, Jagmohan Tyagi
In this note, we establish the existence of a positive solution and its stability to the following problem $$Δ_{\mathbb{H}^n}^2u=a(ξ)u-f(ξ,u)\text{ in }Ω, \,\,\, u|_{\partialΩ} = 0…