Calculus of Variations on Hypergraphs

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Mengqiu Shao, Yulu Tian, Liang Zhao

Published: 20 Jan 2025, Last Modified: 26 Jan 2026OpenReview Archive Direct UploadEveryoneCC BY 4.0
Abstract: We have established a coherent framework for applying variational methods to partial differential equations on hypergraphs, which includes the propositions of calculus and function spaces on hypergraphs. Several results related to the maximum principle on hypergraphs have also been proven. As applications, we demonstrated how these can be used to study partial differential equations on hypergraphs.