We study some properties of De Giorgi's minimal barriers and local minimal barriers for geometric flows of subsets of R-n. Concerning evolutions of the form partial derivative u/partial derivative t + F(del u, del(2)u) = 0, we prove a representation result for the minimal barrier M(E, F-F) when F is not degenerate elliptic; namely, we show that M(E, F-F) = M(E, FF+), where F+ is the smallest degenerate elliptic function above F. We also characterize the disjoint sets property and the joint sets property in terms of the Function F.

Minimal Barriers for Geometric Evolutions

NOVAGA, MATTEO
1997

Abstract

We study some properties of De Giorgi's minimal barriers and local minimal barriers for geometric flows of subsets of R-n. Concerning evolutions of the form partial derivative u/partial derivative t + F(del u, del(2)u) = 0, we prove a representation result for the minimal barrier M(E, F-F) when F is not degenerate elliptic; namely, we show that M(E, F-F) = M(E, FF+), where F+ is the smallest degenerate elliptic function above F. We also characterize the disjoint sets property and the joint sets property in terms of the Function F.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/2507938
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