Ujjal Das

activity

20182025

most citedOn the optimization of the first weighted eigenvalue

10 citations · 18 across the 13 of their papers we have counts for

collaborators

13 papers

math.AP2025

An optimal fractional Hardy inequality on the discrete half-line

Ujjal Das, Rubén de la Fuente-Fernández

In the context of Hardy inequalities for the fractional Laplacian $(- Δ_{N})^{σ}$ on the discrete half-line $N$ , we provide an optimal Hardy-weight $W^{\mathrm{op}}_…

math.AP2023

Characterizations of compactness and weighted eigenvalue problem associated with fractional Hardy-type inequalities

Ujjal Das, Rohit Kumar, Abhishek Sarkar

In this article, we consider the following fractional {Hardy-type} inequality: \begin{align} \label{Fractional Hardy_abst} \int_{\mathbb{R}^N} |w(x)||u(x)|^p \mathrm{d}x \leq C \in…

math.AP2023

A lower bound for the weighted-Hardy constant for domains satisfying a uniform exterior cone condition

Ujjal Das, Yehuda Pinchover

We consider weighted Hardy inequalities involving the distance function to the boundary of a domain in the $N$ -dimensional Euclidean space with nonempty boundary. We give a lower b…

math.AP2023

On Weighted Orlicz-Sobolev inequalities

T V Anoop, Ujjal Das, Subhajit Roy

Let $Ω$ be an open subset of $R^{N}$ with $N \geq 2.$ We identify various classes of Young functions $Φ$ and $Ψ$ , and function spaces for a weight function $g$ so that the fo…

math.AP2023

On existence of minimizers for weighted $L^{p}$ -Hardy inequalities on $C^{1, γ}$ -domains with compact boundary

Ujjal Das, Yehuda Pinchover, Baptiste Devyver

Let $p \in (1, \infty)$ , $α \in R$ , and $Ω ⊊ R^{N}$ be a $C^{1, γ}$ -domain with a compact boundary $\partial Ω$ , where $γ \in (0, 1]$ . Denote by $δ_{Ω} (x)$ the dis…

math.AP2022★ 1 cited

On the fourth order semipositone problem in $R^{N}$

Nirjan Biswas, Ujjal Das, Abhishek Sarkar

For $N \geq 5$ and $a > 0$ , we consider the following semipositone problem \begin{align*} Δ^2 u= g(x)f_a(u) \text { in } \mathbb{R}^N, \, \text{ and } \, u \in \mathcal{D}^{2,2}(\mat…

math.AP2022

On the generalised Brezis-Nirenberg problem

T. V. Anoop, Ujjal Das

For $p \in (1, N)$ and a domain $Ω$ in $R^{N}$ , we study the following quasi-linear problem involving the critical growth: \begin{eqnarray*} -Δ_p u - μg|u|^{p-2}u = |u|^{p^{…

math.AP2022

The space of Hardy-weights for quasilinear equations: Maz'ya-type characterization and sufficient conditions for existence of minimizers

Ujjal Das, Yehuda Pinchover

Let $p \in (1, \infty)$ and $Ω \subset R^{N}$ be a domain. Let $A := (a_{ij}) \in L_{loc}^{\infty} (Ω; R^{N \times N})$ be a symmetric and locally uniformly posi…

math.AP2021★ 10 cited

On the optimization of the first weighted eigenvalue

Nirjan Biswas, Ujjal Das, Mrityunjoy Ghosh

For $N \geq 2$ , a bounded smooth domain $Ω$ in $R^{N}$ , and $g_{0}, V_{0} \in L_{l oc}^{1} (Ω)$ , we study the optimization of the first eigenvalue for the following weighted eigenval…

math.AP2020★ 3 cited

Admissible function spaces for weighted Sobolev inequalities

T. V. Anoop, Nirjan Biswas, Ujjal Das

Let $k, N \in N$ with $1 \leq k \leq N$ and let $Ω = Ω_{1} \times Ω_{2}$ be an open set in $R^{k} \times R^{N - k}$ . For $p \in (1, \infty)$ and $q \in (0, \infty),$ we co…

math.AP2020

On weighted logarithmic-Sobolev & logarithmic-Hardy inequalities

Ujjal Das

For $N \geq 3$ and $p \in (1, N)$ , we look for $g \in L_{l oc}^{1} (R^{N})$ that satisfies the following weighted logarithmic Sobolev inequality: \begin{equation*} \int_{\mathbb{…

math.AP2019★ 1 cited

The compactness and the concentration compactness via $p$ -capacity

T. V. Anoop, Ujjal Das

For $p \in (1, N)$ and $Ω \subseteq R^{N}$ open, the Beppo-Levi space $D_{0}^{1, p} (Ω)$ is the completion of $C_{c}^{\infty} (Ω)$ with respect to the norm $\left( \int_Ω|\…

math.AP2018★ 3 cited

On the Generalized Hardy-Rellich Inequalities

T. V. Anoop, Ujjal Das, Abhishek Sarkar

In this article, we look for the weight functions (say $g$ ) that admits the following generalized Hardy-Rellich type inequality: $ \int_Ω g(x) u^2 dx \leq C \int_Ω |Δu|^2 dx, \fora…

An optimal fractional Hardy inequality on the discrete half-line

Characterizations of compactness and weighted eigenvalue problem associated with fractional Hardy-type inequalities

A lower bound for the weighted-Hardy constant for domains satisfying a uniform exterior cone condition

On Weighted Orlicz-Sobolev inequalities

On existence of minimizers for weighted Lp-Hardy inequalities on C1,γ-domains with compact boundary

On the fourth order semipositone problem in RN

On the generalised Brezis-Nirenberg problem

The space of Hardy-weights for quasilinear equations: Maz'ya-type characterization and sufficient conditions for existence of minimizers

On the optimization of the first weighted eigenvalue

Admissible function spaces for weighted Sobolev inequalities

On weighted logarithmic-Sobolev & logarithmic-Hardy inequalities

The compactness and the concentration compactness via p-capacity

On the Generalized Hardy-Rellich Inequalities

On existence of minimizers for weighted $L^{p}$ -Hardy inequalities on $C^{1, γ}$ -domains with compact boundary

On the fourth order semipositone problem in $R^{N}$

The compactness and the concentration compactness via $p$ -capacity