Maximum principles and related problems for a class of nonlocal extremal operators
Isabeau Birindelli, Giulio Galise, Delia Schiera
TL;DR
This paper investigates maximum principles and eigenvalues for a class of degenerate nonlinear operators involving fractional diffusion, establishing foundational properties and their interrelations.
Contribution
It introduces new results on comparison and maximum principles for nonlocal extremal operators with fractional diffusion, linking these principles to principal eigenvalues.
Findings
Comparison principles are valid for the studied operators.
Maximum principles are established under certain conditions.
Principal eigenvalues are characterized and related to maximum principles.
Abstract
We study the validity of the comparison and maximum principles, and their relation with principal eigenvalues, for a class of degenerate nonlinear operators that are extremal among operators with one dimensional fractional diffusion.
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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Nonlinear Partial Differential Equations · Differential Equations and Boundary Problems