T. Anoop

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20152022

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math.AP2025

Reverse Faber-Krahn inequalities for the Logarithmic potential operator

T. V. Anoop, Jiya Rose Johnson

For a bounded open set $Ω \subset R^{2},$ we consider the largest eigenvalue $τ_{1} (Ω)$ of the Logarithmic potential operator $L$ . If $d iam (Ω) \leq 1$ , we prove reverse…

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.AP2019

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

On the reverse Faber-Krahn inequalities

T. V. Anoop, K. Ashok Kumar

Payne-Weinberger showed that \textit{`among the class of membranes with given area $A$ , free along the interior boundaries and fixed along the outer boundary of given length $L_{0}$ ,…

math.AP2015

On the structure of the second eigenfunctions of the p-Laplacian on a ball

T. V. Anoop, P. Drabek, Sarath Sasi

In this paper, we prove that the second eigenfunctions of the $p$ -Laplacian, $p > 1$ , are not radial on the unit ball in $R^{N},$ for any $N \geq 2.$ Our proof relies on the var…