Ujjal Das

activity

20192022

collaborators

4 papers

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.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

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