57 citations · 65 across the 14 of their papers we have counts for
16 papers
A constrained log-HLS inequality and its associated Wasserstein flow
Monideep Ghosh, Debabrata Karmakar, Reetaj Sinha +1
We study a log-Hardy-Littlewood-Sobolev (log-HLS) inequality under constraints and a naturally induced Wasserstein flow. The constrained log-HLS inequality is dual, in a variationa…
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…
A scalar field equation on hyperbolic space with indefinite sign nonlinearity
Debabrata Karmakar, Atanu Manna, Bhakti Bhusan Manna
In this article, we study threshold phenomena for the semilinear double-power elliptic equation $$-Δ_{\mathbb{B}^N} u - λu = |u|^{p-1}u - |u|^{q-1}u, \quad u \in H^1(\mathbb{B}^N),…
Quantitative stability for the conformally invariant Chang-Gui inequality on the exponentiation of functions on the sphere
Monideep Ghosh, Debabrata Karmakar
In this work, we focus on a recent variant of the Trudinger-Moser-Onofri inequality introduced by S. Y. Alice Chang and Changfeng Gui \cite{CG-2023}: \begin{align*} α\int_{\mathbb{…
Existence of Bianchi-Egnell stability extremizer for the Hardy-Sobolev inequality
Souptik Chakraborty, Monideep Ghosh, Debabrata Karmakar
In this article, we prove the best Bianchi-Egnell constant for the Hardy-Sobolev (HS) inequality \begin{align*} C_{\tiny\mbox{BE}}(γ) := \inf_{u \ \small \mbox{not an optimizer}} \…
A note on the log-perturbed Brézis-Nirenberg problem on the hyperbolic space
Monideep Ghosh, Anumol Joseph, Debabrata Karmakar
We consider the log-perturbed Brézis-Nirenberg problem on the hyperbolic space \begin{align*} Δ_{\mathbb{B}^N}u+λu +|u|^{p-1}u+θu \ln u^2 =0, \ \ \ \ u \in H^1(\mathbb{B}^N), \ u >…
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…
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 …
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…
On the critical mass Patlak-Keller-Segel system for multi-species populations: global existence and infinite time aggregation
Debabrata Karmakar, Gershon Wolansky
We study the global in time existence and long time asymptotics of solutions to the parabolic-elliptic Patlak-Keller-Segel system for the multi-species populations in the whole Euc…
On Patlak-Keller-Segel system for several populations: a gradient flow approach
Debabrata Karmakar, Gershon Wolansky
We study the global in time existence of solutions to the parabolic-elliptic Patlak-Keller-Segel system of multi-species populations. We prove that if the initial mass satisfies an…
Self-similar solutions of decaying Keller-Segel systems for several populations
Debabrata Karmakar, Gershon Wolansky
It is known that solutions of the parabolic elliptic Keller-Segel equations in the two dimensional plane decay, as time goes to infinity, provided the initial data admits sub-criti…
Quantum walks and non-Abelian discrete gauge theory
Pablo Arnault, Giuseppe Di Molfetta, Marc Brachet +1
A new family of discrete-time quantum walks (DTQWs) on the line with an exact discrete gauge invariance is introduced. It is shown that the continuous limit of these DTQWs,…
Adams' inequality with exact growth in the hyperbolic space and Lions lemma
Debabrata Karmakar
In this article we prove Adams inequality with exact growth condition in the four dimensional hyperbolic space \begin{align} \int_{\mathbb{H}^4} \frac{e^{32 π^2 u^2…
Adam's Inequality on the Hyperbolic space
Debabrata Karmakar, Kunnath Sandeep
In this article we establish an Adam's Inequality in the Hyperbolic space. As an application we will also prove the asymptotic behaviour of the best constants in the Sobolev inequa…
Existence Results For Semilinear Problems in the Two Dimensional Hyperbolic Space Involving Critical Growth
Debabrata Karmakar, Debdip Ganguly
We consider semilinear elliptic problems on two-dimensional hyperbolic space involving critical growth. We first establish the Palais-Smale(P-S) condition and using (P-S) condition…