Author:
Stuvard Salvatore,Tonegawa Yoshihiro
Abstract
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.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Analysis
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