Given two intersecting sets of finite perimeter, and , with unit normals and respectively, we obtain a bound on the integral of over the reduced boundary of inside . This bound depends only on the perimeter of . For any vector field with the property that and div is a (signed) Radon measure, we obtain bounds on the flux of over the portion of the reduced boundary of inside . These results are then applied to study the limit of surfaces with perimeter growing to infinity.
Cite this article
Ido Bright, Monica Torres, The integral of the normal and fluxes over sets of finite perimeter. Interfaces Free Bound. 17 (2015), no. 2, pp. 245–262DOI 10.4171/IFB/341