Young functions on varifolds. Part I. Functional analytic foundations

2025/10/07 by Chou, Hsin-Chuang
#28A35 (Primary) 60B10 #46A13 (Secondary) #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2510.05639

Abstract

In this paper, we study Young functions, a measure-theoretic model for multiple-valued functions, and the convergence of pairs of measures and Young functions via their associated graph measures. This setting allows us to study the convergence of pairs of surfaces and functions thereon, and a compactness theorem is immediate. To develop notions of differentiability of Young functions in the upcoming papers, we also introduce and investigate several test function spaces.

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