Physics

Operator (biology)

Pure mathematics

Mathematics

Transcription factor

Gene

Banach space

Mathematical analysis

Boundary value problem

Repressor

Eigenvalues and eigenvectors

Neumann boundary condition

Von Neumann's theorem

Chemistry

Quantum mechanics

Applied mathematics

Biochemistry

Von Neumann architecture

Finite-rank operator

Asymptotic Analysis

We consider here a new type of mixed local and nonlocal equation under suitable Neumann conditions. We discuss the spectral properties associated to a weighted eigenvalue problem and present a global bound for subsolutions. The Neumann condition that we take into account comprises, as a particular case, the one that has been recently introduced in (Rev. Mat. Iberoam. 33(2) (2017), 377–416). Also, the results that we present here find a natural application to a logistic equation motivated by biological problems that has been recently considered in (Dipierro, Proietti Lippi and Valdinoci (2021)).

Linear theory for a mixed operator with Neumann conditions