Title | Dirichlet energy-minimizers with analytic boundary |
Publication Type | Journal Article |
Year of Publication | 2023 |
Authors | De Lellis C, Zhao Z |
Journal | Indiana Univ. Math. J.. |
Volume | 72 |
Start Page | 1367 |
Type of Article | Q-valued |
Abstract | In this paper, we consider multi-valued graphs with a prescribed real analytic interface that minimize the Dirichlet energy. Such objects arise as a linearized model of area minimizing currents with real analytic boundaries and our main result is that their singular set is discrete in 2 dimensions. This confirms (and provides a first step to) a conjecture by B. White \cite{White97} that area minimizing 2-dimensional currents with real analytic boundaries have a finite number of singularities. We also show that, in any dimension, Dirichlet energy-minimizers with a C1 boundary interface are H\"older continuous at the interface. |
Notes | Indiana Univ. Math. J. 72 (2023), no. 4, 1367-1428 |
URL | http://www.iumj.indiana.edu/IUMJ/FULLTEXT/2023/72/8832 |
DOI | 10.1512/iumj.2023.72.8832 |
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