On representation of boundary integrals involving the mean curvature for mean-convex domains

2013/03/18 by Yoshikazu Giga, Giga, Yoshikazu, Giovanni Pisante +1
Computer Science · Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Analytic and geometric function theory #FOS: Mathematics #Holomorphic and Operator Theory #Nonlinear Partial Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1303.4281

arxiv created 2013/03/18 · openalex publication_date 2013/03/18 · arxiv updated 2013/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a mean-convex domain Ω⊂ \Rⁿ with boundary of class C^2,1, we provide a representation formula for a boundary integral of the type ∫_{∂ Ω} f(k(x)) dH^n-1 where k≥ 0 is the mean curvature of ∂ Ω and f is non-increasing and sufficiently regular, in terms of volume integrals and defect measure on the ridge set.

Citations

• Sublinear functions of measures and variational integrals

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