14 citations · 40 across the 21 of their papers we have counts for
14 papers · 1 filter
On the stability of eigenvalues of varying bilinear forms in abstract Hilbertian settings and applications
Andrea Bisterzo, Roberto Ognibene, Prasun Roychowdhury +1
The aim of the present paper is to develop a spectral perturbation theory from a higher perspective. More precisely, we consider a one-parameter family of varying bilinear forms, e…
Profile decomposition and multiple positive solutions for the perturbed CR Yamabe equation on the Heisenberg group
Riju Basak, Souptik Chakraborty, Tapendu Rana +1
In this article, we study an inhomogeneous critical nonlinear equation involving the sub-Laplacian on the Heisenberg group . We prove the multiplicity of positive solu…
Sharp Quantitative Forms of the Hardy Inequality on Cartan-Hadamard Manifolds via Sobolev-Lorentz Embeddings
Avas Banerjee, Debdip Ganguly, Prasun Roychowdhury
In this article, we investigate the quantitative form of the classical Hardy inequality. In our first result, we prove the following quantitative bound under the assumption that th…
Extremizer Stability of Higher-order Hardy-Rellich inequalities for Baouendi--Grushin vector fields
Avas Banerjee, Riju Basak, Prasun Roychowdhury
In this paper, we improve the -Rellich and Hardy-Rellich inequalities in the setting of radial Baouendi-Grushin vector fields. We establish an identity relating the subcritica…
On sharp constants in higher order Adams-Cianchi inequalities
Prasun Roychowdhury, Daniel Spector
The main results of this paper are the establishment of sharp constants for several families of critical Sobolev embeddings. These inequalities were pioneered by David R. Adams, wh…
Hardy and Rellich identities and inequalities for Baouendi-Grushin operators via spherical vector fields
Debdip Ganguly, K. Jotsaroop, Prasun Roychowdhury
For Baouendi-Grushin vector fields, we prove Hardy, Hardy-Rellich, and Rellich identities and inequalities with sharp constants. Our explicit remainder terms significantly improve…
Critical, stability and higher-order analysis for Hardy type inequalities on Cartan-Hadamard manifolds
Prasun Roychowdhury, Durvudkhan Suragan, Nurgissa Yessirkegenov
In this paper, we focus on three main objectives related to Hardy-type inequalities on Cartan-Hadamard manifolds. Firstly, we explore critical Hardy-type inequalities that contain…
Classification of radial solutions to on Riemannian models
Elvise Berchio, Alberto Ferrero, Debdip Ganguly +1
We provide a complete classification with respect to asymptotic behaviour, stability and intersections properties of radial smooth solutions to the equation on Riemann…
Improved Poincaré-Hardy inequalities on certain subspaces of the Sobolev space
Debdip Ganguly, Prasun Roychowdhury
We prove an improved version of Poincaré-Hardy inequality in suitable subspaces of the Sobolev space on the hyperbolic space via Bessel pairs. As a consequence, we obtain a new Har…
Stochastic completeness and -Liouville property for second-order elliptic operators
Debdip Ganguly, Yehuda Pinchover, Prasun Roychowdhury
Let be a linear, second-order, elliptic operator with real coefficients defined on a noncompact Riemannian manifold and satisfies in . Assume further that adm…
Hardy-Rellich and second order Poincaré identities on the hyperbolic space via Bessel pairs
Elvise Berchio, Debdip Ganguly, Prasun Roychowdhury
We prove a family of Hardy-Rellich and Poincaré identities and inequalities on the hyperbolic space having, as particular cases, improved Hardy-Rellich, Rellich and second order Po…
On ergodic control problem for viscous Hamilton--Jacobi equations for weakly coupled elliptic systems
Ari Arapostathis, Anup Biswas, Prasun Roychowdhury
In this article we study ergodic problems in the whole space for weakly coupled systems of viscous Hamilton-Jacobi equations with coercive right-hand sides. The Hami…
Generalized principal eigenvalues on of second order elliptic operators with rough nonlocal kernels
Ari Arapostathis, Anup Biswas, Prasun Roychowdhury
We study the generalized eigenvalue problem on the whole space for a class of integro-differential elliptic operators. The nonlocal operator is over a finite measure, but this has…
Generalized principal eigenvalues of convex nonlinear elliptic operators in
Anup Biswas, Prasun Roychowdhury
We study the generalized eigenvalue problem in for a general convex nonlinear elliptic operator which is locally elliptic and positively -homogeneous. Generalizin…