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math.AP2024
Existence results for mixed local and nonlocal elliptic equations involving singularity and nonregular data
Souvik Bhowmick, Sekhar Ghosh
In this paper, we prove the existence of weak, veryweak and duality solutions to a class of elliptic problems involving singularity and measure data which is given by: $-Δu+(-Δ)^s…
math.AP2024★ 1 cited
Subelliptic Nonlocal Brezis-Nirenberg Problems on Stratified Lie Groups
Sekhar Ghosh, Vishvesh Kumar, Michael Ruzhansky
In this paper, we investigate the subelliptic nonlocal Brezis-Nirenberg problem on stratified Lie groups involving critical nonlinearities, namely, \begin{align*} (-Δ_{\mathbb{G},…
math.AP2024
A weighted eigenvalue problem for mixed local and nonlocal operators with potential
R. Lakshmi, Ratan Kr. Giri, Sekhar Ghosh
We study an {\it indefinite weighted eigenvalue problem} for an operator of {\it mixed-type} (that includes both the classical {\it -Laplacian} and the {\it fractional -Lapla…