T. Anoop

activity

20152026

most citedOn the strict monotonicity of the first eigenvalue of the

p

-Laplacian on annuli

17 citations · 66 across the 22 of their papers we have counts for

collaborators

22 papers

math.AP2026

On the Hersch-Weinberger inequality in higher dimensions

T. V. Anoop, Vladimir Bobkov, Mrityunjoy Ghosh +1

We investigate a reverse Faber-Krahn type inequality for the Robin Laplacian in a bounded smooth domain $Ω \subset R^{N}$ whose boundary has two connected components. We prov…

math.AP2026

On the weighted logarithmic potential operator

T. V. Anoop, Jiya Rose Johnson

For a bounded open set $Ω \subset R^{N}$ with $N \geq 2$ , and for positive continuous functions $w, g$ on $Ω$ , we consider the weighted eigenvalue problem \begin{equat…

math.AP2025

Reverse Faber-Krahn inequality for planar doubly connected domains

T. V. Anoop, Vladimir Bobkov, Mrityunjoy Ghosh

We prove that among all doubly connected and elastically supported planar membranes $Ω$ with prescribed values of the area $∣Ω∣$ and the lengths of the inner and outer boundaries $…

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.AP2024

Neumann domains of planar analytic eigenfunctions

T. V. Anoop, Vladimir Bobkov, Mrityunjoy Ghosh

Along with the partition of a planar bounded domain $Ω$ by the nodal set of a fixed eigenfunction of the Laplace operator in $Ω$ , one can consider another natural partition of $Ω$ …

math.AP2024

On Fractional Orlicz-Hardy Inequalities

T. V. Anoop, Prosenjit Roy, Subhajit Roy

We establish the weighted fractional Orlicz-Hardy inequalities for various Orlicz functions. Further, we identify the critical cases for each Orlicz function and prove the weighted…

math.AP2023★ 1 cited

Reverse Faber-Krahn and Szego-Weinberger type inequalities for annular domains under Robin-Neumann boundary conditions

T. V. Anoop, Vladimir Bobkov, Pavel Drabek

Let $τ_{k} (Ω)$ be the $k$ -th eigenvalue of the Laplace operator in a bounded domain $Ω$ of the form $Ω_{out} ∖ B_{α}$ under the Neumann boundary condition on…

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.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★ 1 cited

Reverse Faber-Krahn inequalities for Zaremba problems

T. V. Anoop, Mrityunjoy Ghosh

Let $Ω$ be a multiply-connected domain in $R^{n}$ ( $n \geq 2$ ) of the form $Ω = Ω_{out} ∖ Ω_{in} ˉ .$ Set $Ω_{D}$ to be either $Ω_{out}$ or $Ω_{\te…

math.AP2022★ 7 cited

Domain variations of the first eigenvalue via a strict Faber-Krahn type inequality

T. V. Anoop, K. Ashok Kumar

For $d \geq 2$ and $\frac{2 d + 2}{d + 2} < p < \infty$ , we prove a strict Faber-Krahn type inequality for the first eigenvalue $λ_{1} (Ω)$ of the $p$ -Laplace operator on a bounded Lipschi…

math.DG2022

Szegö-Weinberger type inequalities for symmetric domains in simply connected space forms

T. V. Anoop, Sheela Verma

We consider the Neumann eigenvalue problem for Laplacian on a bounded multi-connected domain contained in simply connected space forms. Under certain symmetry assumptions on the do…

math.AP2021★ 2 cited

Szegő-Weinberger type inequalities for symmetric domains with holes

T. V. Anoop, Vladimir Bobkov, Pavel Drabek

Let $μ_{2} (Ω)$ be the first positive eigenvalue of the Neumann Laplacian in a bounded domain $Ω \subset R^{N}$ . It was proved by Szegő for $N = 2$ and by Weinberger for $N \geq 2$ …

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 global bifurcation for the nonlinear Steklov problems

T. V. Anoop, Nirjan Biswas

For $p \in (1, \infty),$ for an integer $N \geq 2$ and for a bounded Lipschitz domain $Ω$ , we consider the following nonlinear Steklov bifurcation problem \begin{equation*} \begin{…

math.AP2020★ 15 cited

A shape variation result via the geometry of eigenfunctions

T. V. Anoop, K. Ashok Kumar, S Kesavan

We discuss some of the geometric properties, such as the foliated Schwarz symmetry, the monotonicity along the axial and the affine-radial directions, of the first eigenfunctions o…

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

Neumann eigenvalue problems on the exterior domains

T. V. Anoop, Nirjan Biswas

For $p \in (1, \infty)$ , we consider the following weighted Neumann eigenvalue problem on $B_{1}^{c}$ , the exterior of the closed unit ball in $R^{N}$ : \begin{equation}\label{Neumann eqn…

math.AP2018★ 13 cited

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.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…

math.AP2016★ 17 cited

On the strict monotonicity of the first eigenvalue of the $p$ -Laplacian on annuli

T. V. Anoop, Vladimir Bobkov, Sarath Sasi

Let $B_{1}$ be a ball in $R^{N}$ centred at the origin and $B_{0}$ be a smaller ball compactly contained in $B_{1}$ . For $p \in (1, \infty)$ , using the shape derivative method, we s…

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…