Abstract:Let V be a finite set, E ⊂ 2 V be a set of hyperedges, and w ∶ E → (0, ∞) be an edge weight. On the (wighted) hypergraph G = (V, E, w), we can define a multivalued nonlinear operator L G,p (p ∈ [1, ∞)) as the subdifferential of a convex function on R V , which is called "hypergraph p-Laplacian." In this article, we first introduce an inequality for this operator L G,p , which resembles the Poincaré-Wirtinger inequality in PDEs. Next, we consider an ordinary differential equation on R V governed by L G,p , whic… Show more
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