21 citations · 48 across the 18 of their papers we have counts for
19 papers
A fractional Brezis-Nirenberg problem with multipolar Hardy potentials
Debangana Mukherjee
We study a fractional Brezis--Nirenberg problem on a bounded domain with finitely many Hardy potentials centered at distinct points , with masses $μ_1,\dots,μ_k\geq…
Critical fractional -Hardy Sobolev equations: Global compactness and multiplicity of positive solutions
Nirjan Biswas, Souptik Chakraborty, Debangana Mukherjee
We study the critical fractional -Hardy-Sobolev equation \begin{equation}\tag{}\label{a-main} (-Δ_p)^s u -μ\dfrac{|u|^{p-2}u}{|x|^{sp}}=\dfrac{|u|^{p^*_s(α)-2}u}{|x…
Nonlocal Tikhonov Regularization: Hilbert Scales, Explicit Rates, and the Classical Limit
Debangana Mukherjee, Akash Ashirbad Panda
We study fractional-Sobolev Tikhonov regularization for linear inverse problems on a bounded Lipschitz domain. The regularization penalty is generated by the restricted Dirichlet f…
Equivalence of weak and viscosity solutions for nonlocal p-Laplace type equations on the Heisenberg group
Debangana Mukherjee, Vivek Tewary
We establish the equivalence between weak and viscosity solutions for a broad class of nonlocal -Laplace type equations on the Heisenberg group whose kernels satisfy standard sy…
On fractional critical problems with multi-polar Hardy potentials
Edoardo Mainini, Debangana Mukherjee, Roberto Ognibene
We investigate the existence of positive solutions to fractional equations presenting a double criticality: a multi-polar Hardy-type potential and a Sobolev critical nonlinearity.…
Non-homogeneous -fractional Laplacian systems with lack of compactness
Debangana Mukherjee, Tuhina Mukherjee
The present paper studies the existence of weak solutions for the following type of non-homogeneous system of equations \begin{equation*} (S) \left\{\begin{aligned} (-Δ)^{s_1}_{p_1…
On the study of semilinear non-local elliptic systems
Debangana Mukherjee, Debopriya Mukherjee
The purpose of this paper is to study the existence of solutions for semilinear elliptic system driven by fractional Laplacian and establish some new existence results which are ob…
On the existence of three non-negative solutions for a -Laplacian system
Debangana Mukherjee, Tuhina Mukherjee
The present paper studies the existence of weak solutions for \begin{equation*} (\mathcal{P}) \left\{\begin{aligned} (-Δ)^{s_1}_{p_1} u &=\la f_1\,(x,u,v) +g_1(x,u) \,\mbox{ in }\,…
Multiplicity results for non-local elliptic problems with jumping nonlinearity
Debangana Mukherjee
The present paper studies the fractional -Laplacian boundary value problems with jumping nonlinearities at zero or infinity and obtain the existence of multiple solutions and si…
On the existence of multiple solutions for fractional Brezis Nirenberg type equations
Debangana Mukherjee
The present paper studies the non-local fractional analogue of the famous paper of Brezis and Nirenberg in [4]. Namely, we focus on the following model, $$\begin{align*}\left(\math…
Uniqueness of the critical point for semi-stable solution in
Fabio De Regibus, Massimo Grossi, Debangana Mukherjee
In this paper we show the uniqueness of the critical point for \emph{semi-stable} solutions of the problem $$\begin{cases} -Δu=f(u)&\text{in }Ω\\ u>0&\text{in }Ω\\ u=0&\text{on } \…
A Carleman estimate for the fractional heat equation and its application in final state observability
Erika Hausenblas, Debangana Mukherjee
In the paper, we show a global Carleman estimate for the non-local heat equation. To be more precise, let $Ω\subset\RR^d$ be a bounded domain and $\CO\subsetΩ$ an open subdomain, $…
On fractional multi-singular Schrödinger operators: positivity and localization of binding
Veronica Felli, Debangana Mukherjee, Roberto Ognibene
In this work we investigate positivity properties of nonlocal Schrödinger type operators, driven by the fractional Laplacian, with multipolar, critical, and locally homogeneous pot…
Nonlocal scalar field equations: qualitative properties, asymptotic profiles and local uniqueness of solutions
Mousomi Bhakta, Debangana Mukherjee
We study the nonlocal scalar field equation with a vanishing parameter \[ \left\{\begin{array}{lll} (-Δ)^s u+εu &=|u|^{p-2}u -|u|^{q-2}u \quad\text{in}\quad\mathbb{R}^N \\ u >0, &…
Multiplicity results for fractional elliptic equations involving critical nonlinearities
Mousomi Bhakta, Debangana Mukherjee
In this paper we prove the existence of infinitely many nontrivial solutions for the class of fractional elliptic equations involving concave-critical nonlinearities in…
Sign changing solutions of p-fractional equations with concave-convex nonlinearities
Mousomi Bhakta, Debangana Mukherjee
In this article we study the existence of sign changing solution of the following p-fractional problem with concave-critical nonlinearities: \begin{eqnarray*} (-Δ)^s_pu &=& μ|u|^{q…
Profile of solutions for nonlocal equations with critical and supercritical nonlinearities
Mousomi Bhakta, Debangana Mukherjee, Sanjiban Santra
We study the fractional laplacian problem (-Δ)^s u &=& u^p -εu^q \quad\text{in }\quad Ω, u &\in& H^s(Ω)\cap L^{q+1}(Ω),u &>&0 \quad\text{in }\quad Ω, u&=&0 \quad\text{in}\quad \mat…
Semilinear nonlocal elliptic equations with critical and supercritical exponents
Mousomi Bhakta, Debangana Mukherjee
We study the problem \begin{eqnarray*} (-Δ)^s u &=& u^p - u^q \quad\text{in }\quad \mathbb{R}^N, u &\in& \dot{H}^s(\mathbb{R}^N)\cap L^{q+1}(\mathbb{R}^N), u&>0& \quad\text{in}\qua…
Multiplicity results and sign changing solutions of non-local equations with concave-convex nonlinearities
Mousomi Bhakta, Debangana Mukherjee
In this paper we prove the existence of infinitely many nontrivial solutions of the following equations driven by a nonlocal integro-differential operator with concave-convex…