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Rectifiability and almost everywhere uniqueness of the blow-up for the vectorial Bernoulli free boundaries

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arxiv 2107.12485 v2 pith:QO74NAET submitted 2021-07-26 math.AP

Guido De Philippis , Max Engelstein , Luca Spolaor , Bozhidar Velichkov This is my paper
classification math.AP
keywords almostapplicationblow-upeverywherefreerectifiabilityuniquenessvectorial
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We prove that for minimizers of the vectorial Alt-Caffarelli functional the two-phase singular set of the free boundary is rectifiable and the blow-up is unique almost everywhere on it. While the first conclusion is an application of the recent techniques developed by Naber and Valtorta, the uniqueness part follows from the rectifiability and a new application of the Alt-Caffarelli-Friedman monotonicity formula.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. One-phase Free Boundary Problems on RCD Metric Measure Spaces

    math.AP 2021-12 unverdicted novelty 7.0 of 10

    Existence, Lipschitz regularity, and almost-(N-1)-manifold structure of free boundaries are proved for one-phase Bernoulli problems on non-collapsed RCD(K,N) spaces.

  2. On a Multiphase Vectorial Bernoulli Free Boundary Problem

    math.AP 2026-05 unverdicted novelty 6.0 of 10

    Minimizers of the multiphase vectorial Bernoulli functional exist, are locally Lipschitz, avoid triple points on the free boundary, and have C^{1,η} regularity near two-phase and branching points.

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