We study some relations between the concepts of perimeter, Hausdorff measure, and Minkowsky content, when Rn is endowed with a convex Finsler metric depending in a continuous way on the position. We show some connections with the theory of Gamma-convergence and with the anisotropic motion of a smooth hypersurface by mean curvature.
Paolini, M., Bellettini, G., Venturini, S., Some results on surface measures in Calculus of Variations, <<ANNALI DI MATEMATICA PURA ED APPLICATA>>, 1996; (170): 329-359. [doi:10.1007/BF01758994] [http://hdl.handle.net/10807/21410]
Some results on surface measures in Calculus of Variations
Paolini, Maurizio;Bellettini, Giovanni;
1996
Abstract
We study some relations between the concepts of perimeter, Hausdorff measure, and Minkowsky content, when Rn is endowed with a convex Finsler metric depending in a continuous way on the position. We show some connections with the theory of Gamma-convergence and with the anisotropic motion of a smooth hypersurface by mean curvature.
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