Qualitative questions to mixed local-nonlocal elliptic operators

Tyagi, Jagmohan

Qualitative questions to mixed local-nonlocal elliptic operators

Source

Pure and Applied Functional Analysis

ISSN

21893756

Date Issued

2024-01-01

Author(s)

Oza, Priyank

Tyagi, Jagmohan

Volume

9

Issue

1

Abstract

We establish a Lyapunov-type inequality for a class of mixed local- nonlocal operator. We employ solution representation formula for the associated boundary value problem. Furthermore, as an application of the Lyapunov-type inequality, we show a positive lower bound for the generalized principal eigenvalue of the operator.

URI

https://d8.irins.org/handle/IITG2025/29123

Subjects

Dirichlet boundary value problem | Lyapunov inequality | Nonlocal and local operators | Principal eigenvalue | Probabilistic representation