25 citations · 81 across the 32 of their papers we have counts for
38 papers
Gromov-Hausdorff Stability and Rigidity of manifolds via Heisenberg-Pauli-Weyl Uncertainty Principle
Mousomi Bhakta, Debdip Ganguly, Debabrata Karmakar
The classical Heisenberg Pauli Weyl (HPW) inequality exhibits a strong rigidity phenomenon on Riemannian manifolds i.e. on Cartan Hadamard manifolds and those with non-negative Ric…
Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis
Avas Banerjee, Debdip Ganguly, Vivek Sahu
A classical result due to Frank and Seiringer asserts that for , there exists a sharp constant such that $$ δ_{s,p}(u):=\int_{\mathbb{R}^N…
Conformally invariant equations with negative critical exponents on the three dimensional hyperbolic space
Debdip Ganguly, Jungang Li, Guozhen Lu +1
We establish a symmetry result for positive entire solutions with a prescribed growth rate to the following fourth order equation on the 3-dimensional hyperbolic space $\mathbb{H}^…
Logarithmic Sobolev, Poincaré and Beckner Inequalities on Hyperbolic Spaces and Riemannian Manifolds
Anh Xuan Do, Debdip Ganguly, Nguyen Lam +1
We investigate several functional and geometric inequalities on the hyperbolic space , with a primary emphasis on logarithmic Sobolev inequalities, Poincaré inequalit…
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…
Fractional Schrödinger equations with mixed nonlinearities: asymptotic profiles, uniqueness and nondegeneracy of ground states
Mousomi Bhakta, Paramananda Das, Debdip Ganguly
We study the fractional Schrödinger equations with a vanishing parameter: where $s\in…
Poincaré-Sobolev equations with the critical exponent and a potential in the hyperbolic space
Mousomi Bhakta, Debdip Ganguly, Diksha Gupta +1
On the hyperbolic space, we study a semilinear equation with non-autonomous nonlinearity having a critical Sobolev exponent. The Poincaré-Sobolev equation on the hyperbolic space e…
Scale-Dependent Poincaré inequalities, log-Sobolev inequality and the stability of the Heisenberg Uncertainty Principle on the hyperbolic space
Anh Xuan Do, Debdip Ganguly, Nguyen Lam +1
We establish a general scale-dependent Poincaré-Hardy type identity involving a vector field on the hyperbolic space. By choosing suitable parameter, potential and vector field in…
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…
Global compactness result and multiplicity of solutions for a class of critical exponent problem in the hyperbolic space
Mousomi Bhakta, Debdip Ganguly, Diksha Gupta +1
This paper deals with the global compactness and multiplicity of positive solutions to problems of the type $$ -Δ_{\mathbb B^N} u -λu=a(x) |u|^{2^*-2}u+f(x) \quad\text{in } \mathbb…
On a class of elliptic equations with Critical Perturbations in the hyperbolic space
Debdip Ganguly, Diksha Gupta, K. Sreenadh
We study the existence and non-existence of positive solutions for the following class of nonlinear elliptic problems in the hyperbolic space $$ -Δ_{\mathbb{B}^N} u-λu=a(x)u^{p-1}…
Sharp quantitative stability of Struwe's decomposition of the Poincaré-Sobolev inequalities on the hyperbolic space: Part I
Mousomi Bhakta, Debdip Ganguly, Debabrata Karmakar +1
A classical result owing to Mancini and Sandeep [Ann. Sc. Norm. Super. Pisa Cl. Sci. 7 (2008)] asserts that all positive solutions of the Poincaré-Sobolev equation on the hyperboli…
Classification of radial solutions to on Riemannian models
Elvise Berchio, Alberto Ferrero, Debdip Ganguly +1
We provide a complete classification with respect to asymptotic behaviour, stability and intersections properties of radial smooth solutions to the equation on Riemann…
Multiplicity of positive solutions for a class of nonhomogeneous elliptic equations in the hyperbolic space
Debdip Ganguly, Diksha Gupta, K. Sreenadh
The paper is concerned with positive solutions to problems of the type \begin{equation*} -Δ_{\mathbb{B}^N} u - λu = a(x) |u|^{p-1}\;u \, + \, f \, \;\;\text{in}\;\mathbb{B}^{N}, \q…
Sharp quantitative stability of Poincare-Sobolev inequality in the hyperbolic space and applications to fast diffusion flows
Mousomi Bhakta, Debdip Ganguly, Debabrata Karmakar +1
Consider the Poincaré-Sobolev inequality on the hyperbolic space: for every and there exists a best constant …
Improved Poincaré-Hardy inequalities on certain subspaces of the Sobolev space
Debdip Ganguly, Prasun Roychowdhury
We prove an improved version of Poincaré-Hardy inequality in suitable subspaces of the Sobolev space on the hyperbolic space via Bessel pairs. As a consequence, we obtain a new Har…
Existence of high energy positive solutions for a class of elliptic equations in the hyperbolic space
Debdip Ganguly, Diksha Gupta, K. Sreenadh
We study the existence of positive solutions for the following class of scalar field problem on the hyperbolic space $$ -Δ_{\mathbb{H}^N} u - λu = a(x) |u|^{p-1} \, u\;\;\text{in}\…
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…
Non-linear heat equation on the Hyperbolic space: Global existence and finite-time Blow-up
Debdip Ganguly, Debabrata Karmakar, Saikat Mazumdar
We consider the following Cauchy problem for the semi linear heat equation on the hyperbolic space: \begin{align}\label{abs:eqn} \left\{\begin{array}{ll} \partial_{t}u=Δ_{\mathbb{H…
Fractional Hardy equations with critical and supercritical exponents
Mousomi Bhakta, Debdip Ganguly, Luigi Montoro
We study the existence/nonexistence and qualitative properties of the positive solutions to the problem \begin{align*} (-Δ)^s u -θ\frac{u}{|x|^{2s}}&=u^p - u^q \quad\text{in }\,\,…
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…
The Fractional Porous Medium Equation on the hyperbolic space
Elvise Berchio, Matteo Bonforte, Debdip Ganguly +1
We consider the nonlinear degenerate parabolic equation of porous medium type, whose diffusion is driven by the (spectral) fractional Laplacian on the hyperbolic space. We provide…
On some strong Poincaré inequalities on Riemannian models and their improvements
Elvise Berchio, Debdip Ganguly, Prasun Roychowdhury
We prove second and fourth order improved Poincaré type inequalities on the hyperbolic space involving Hardy-type remainder terms. Since theirs l.h.s. only involve the radial part…
Existence and Multiplicity of positive solutions of certain nonlocal scalar field equations
Mousomi Bhakta, Souptik Chakraborty, Debdip Ganguly
We study existence and multiplicity of positive solutions of the following class of nonlocal scalar field equations: \begin{equation} \tag{} \left\{\begin{aligned} (-Δ…