Corrigendum for the comparison theorem in "A new definitions for a class of integro-differential equatons"
M. Arisawa
TL;DR
This paper introduces a nonlocal Jensen-Ishii lemma using convex analysis principles, providing a rigorous foundation for the comparison principle in integro-differential equations.
Contribution
It develops a nonlocal Jensen-Ishii lemma based on Jensen's maximum principle and Alexandrov's theorem, enhancing the theoretical framework for integro-differential equations.
Findings
Established a nonlocal Jensen-Ishii lemma
Provided a rigorous comparison principle argument
Enhanced theoretical tools for integro-differential equations
Abstract
By using the Jensen's maximum principle and the Alexandrov's theorem in the convex analysis, we present the nonlocal version of the Jensen-Ishii lemma, which leads to the precise argument for the comparison principle.
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Taxonomy
TopicsNonlinear Differential Equations Analysis · Fractional Differential Equations Solutions · Functional Equations Stability Results