On representation of boundary integrals involving the mean curvature for mean-convex domains
Yoshikazu Giga, Giovanni Pisante · Scuola Normale Superiore eBooks · 2013
Given a mean-convex domain Ω it (ℝ n with boundary of class C 2,1, we provide a representation formula for a boundary integral of the type $$ \int_{\partial \Omega } {} f(k(x))dH^{n - 1} $$ 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.