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arXiv · 1912.02404

An existence theorem for Brakke flow with fixed boundary conditions

Salvatore Stuvard·Yoshihiro Tonegawa
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Abstract

Consider an arbitrary closed, countably $n$-rectifiable set in a strictly convex $(n+1)$-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 $t \uparrow \infty$, the flow sequentially converges to non-trivial solutions of Plateau's problem in the setting of stationary varifolds.

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Salvatore Stuvard, Yoshihiro Tonegawa. 2019-12-05. An existence theorem for Brakke flow with fixed boundary conditions. https://doi.org/10.1007/s00526-020-01909-z

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