Calculus of Variations on Hypergraphs

• DOI: 10.1007/s12220-024-01892-3
• Publication Date: 2025-01-21T14:27:16Z
• Authors: Mengqiu Shao; Yulu Tian; Liang Zhao
• Keywords: Mathematics - Analysis of PDEs; FOS: Mathematics; Mathematics - Combinatorics; Combinatorics (math.CO); 05C65, 35A15; Analysis of PDEs (math.AP)

20 pages, 25 references<br/>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.<br/>