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arXiv · 2503.23318

A Regularity Theory for Stationary Two-valued Harmonic Functions

Lingxiao Cheng·Lubo Wang
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Abstract

For stationary two-valued harmonic functions with H\"older regularity, we establish their Lipschitz regularity and prove that the nodal set consists of analytic hypersurfaces away from a singular set. The main tools are the Almgren monotonicity formula and the blow-up method. These results are applicable to some limiting problems in segregation models.

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Lingxiao Cheng, Lubo Wang. 2025-03-30. A Regularity Theory for Stationary Two-valued Harmonic Functions. https://arxiv.org/abs/2503.23318

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