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Minimal Barriers for Geometric Evolutions

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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 ∂ u /∂ t + F ([inverted triangle] u , [inverted triangle] 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 , ℱ F + ), 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 .

Document Type: Research Article

Affiliations: 1: Dipartimento di Matematica Applicata "U. Dini,", Universita di Pisa, Via Bonanno 25 bis, Pisa, 56126, Italy 2: Scuola Normale Superiore di Pisa, Piazza dei Cavalieri 7, Pisa, 56100, Italy

Publication date: September 1, 1997

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