An existence theorem for Brakke flow with fixed boundary conditions
2021 ◽
Vol 60
(1)
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Keyword(s):
AbstractConsider an arbitrary closed, countably n-rectifiable set in a strictly convex $$(n+1)$$ ( n + 1 ) -dimensional domain, and suppose that the set has finite n-dimensional Hausdorff measure and the complement is not connected. Starting from this given set, we show that there exists a non-trivial Brakke flow with fixed boundary data for all times. As $$t \uparrow \infty $$ t ↑ ∞ , the flow sequentially converges to non-trivial solutions of Plateau’s problem in the setting of stationary varifolds.
1985 ◽
Vol 26
(2)
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pp. 115-120
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2000 ◽
Vol 11
(08)
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pp. 1057-1078
2016 ◽
Vol 30
(5)
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pp. 82-86
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2004 ◽
Vol 56
(3)
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pp. 529-552
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Keyword(s):
Keyword(s):
1991 ◽
Vol 11
(4)
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pp. 779-786
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