R. Lakshmi

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math.AP2025

On equivalence of weak and viscosity solutions to nonlocal double phase problems with nonhomogeneous data

Sekhar Ghosh, R. Lakshmi, Chao Zhang

This work focuses on the nonhomogeneous nonlocal double phase problem \begin{align*} L_au(x)=f(x,u,D_s^p u, D_{a,t}^q u) \text{ in } Ω, \end{align*} where $Ω \subset R^{N}$ is…

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 $p$ -Laplacian} and the {\it fractional $p$ -Lapla…