Geodesic
The integral of the normal and fluxes over sets of finite perimeter
Ido Bright1 ; Monica Torres2
1University of Washington, Seattle, USA
2Purdue University, West Lafayette, USA
Interfaces and free boundaries, Tome 17 (2015) no. 2, pp. 245-262

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DOI

Given two intersecting sets of finite perimeter, E1​ and E2​, with unit normals ν1​ and ν2​ respectively, we obtain a bound on the integral of ν1​ over the reduced boundary of E1​ inside E2​. This bound depends only on the perimeter of E2​. For any vector field F:Rn→Rn with the property that F∈L∞ and divF is a (signed) Radon measure, we obtain bounds on the flux of F over the portion of the reduced boundary of E1​ inside E2​. These results are then applied to study the limit of surfaces with perimeter growing to infinity.
DOI : 10.4171/ifb/341
Classification : 28-XX
Mots-clés : Gauss–Green theorem, divergence-measure fields, sets of finite perimeter, normal traces, shape optimization, occupational measures

Ido Bright  1   ; Monica Torres  2

1 University of Washington, Seattle, USA
2 Purdue University, West Lafayette, USA 
Ido Bright; Monica Torres. The integral of the normal and fluxes over sets of finite perimeter. Interfaces and free boundaries, Tome 17 (2015) no. 2, pp. 245-262. doi: 10.4171/ifb/341
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     year = {2015},
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     doi = {10.4171/ifb/341},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/341/}
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