4 papers
Optimization for the first weighted eigenvalue of local-nonlocal operators with a potential
R. Lakshmi, Sekhar Ghosh, Ratan Kr. Giri
In this work, we study the optimization problem for the first eigenvalue of mixed local nonlocal operators plus a potential . We begin by investigating the existence and fundame…
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…
Harnack inequality for superposition operators of mixed fractional order
Souvik Bhowmick, Sekhar Ghosh, Vishvesh Kumar +1
The main aim of this paper is to establish the Hölder continuity and the Harnack inequality for weak solutions to Dirichlet problems associated with superposition operators of mixe…
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…