K. Kumar

activity

20182023

most citedA shape variation result via the geometry of eigenfunctions

15 citations · 38 across the 5 of their papers we have counts for

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5 papers · 1 filter

math.AP2023★ 1 cited

Strict Faber-Krahn type inequality for the mixed local-nonlocal operator under polarization

K Ashok Kumar, Nirjan Biswas

Let $Ω \subset R^{d}$ with $d \geq 2$ be a bounded domain of class $C^{1, β}$ for some $β \in (0, 1)$ . For $p \in (1, \infty)$ and $s \in (0, 1)$ , let $Λ_{p}^{s} (Ω)$ be the…

math.AP2023★ 2 cited

Strict monotonicity of the first $q$ -eigenvalue of the fractional $p$ -Laplace operator over annuli

K Ashok Kumar, Nirjan Biswas

Let $B, B^{'} \subset R^{d}$ with $d \geq 2$ be two balls such that $B^{'} \subset\subset B$ and the position of $B^{'}$ is varied within $B$ . For $p \in (1, \infty),$ $s \in (0, 1)$ , an…

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.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.AP2018★ 13 cited

On the reverse Faber-Krahn inequalities