4 papers
A Note on Sharpened Singular Adams-Type Inequalities
Deepak Kumar Mahanta, Tuhina Mukherjee, Abhishek Sarkar
We establish a sharp Adams-type inequality in higher-order function spaces with singular weights on . A sharp singular concentration-compactness principle, improving…
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…
Global branching for semilinear fractional Laplace with sublinear nonlinearity
Jefferson Abrantes, Rohit Kumar, Abhishek Sarkar
This article investigates the existence, nonexistence, and multiplicity of positive solutions to the sublinear fractional elliptic problem . We begin by establishing seve…
Principal eigenvalues for the weighted p-Laplacian and antimaximum principle in
Anumol Joseph, Abhishek Sarkar
We study the existence of principal eigenvalues and principal eigenfunctions for weighted eigenvalue problems of the form: \begin{equation*} - \mbox{div} ( L (x) |\nabla u|^{p-2} \…