From the 1 of 4 linked papers with an AI index.
4 papers
Optimization for the first weighted eigenvalue of local-nonlocal operators with a potential
R. Lakshmi, Sekhar Ghosh, Ratan Kr. Giri
The paper investigates how to choose a potential function to maximize or minimize the first eigenvalue of mixed local‑nonlocal differential operators, proving existence and uniquen…
On weak and viscosity solutions to a nonhomogeneous mixed local-nonlocal equation
R. Lakshmi, Sekhar Ghosh
This paper explores the relationship between weak and viscosity solutions to a nonhomogeneous mixed local and non-local -Laplace equation in a bounded Lipschitz domain in $\math…
Regularity of superposition operators of mixed fractional order
Souvik Bhowmick, Sekhar Ghosh, Vishvesh Kumar +1
We extend the De Giorgi--Nash--Moser theory to superposition operators of mixed fractional operators. In particular, we investigate several regularity properties for this class of…
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 …