Regularity of the nodal set of segregated critical configurations under a weak reflection law

Hugo Tavares; Susanna Terracini

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arXiv · 1002.3822

Regularity of the nodal set of segregated critical configurations under a weak reflection law

Hugo Tavares·Susanna Terracini

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Abstract

We deal with a class of Lipschitz vector functions $U=(u_1,...,u_h)$ whose components are non negative, disjointly supported and verify an elliptic equation on each support. Under a weak formulation of a reflection law, related to the Pohouzaev identity, we prove that the nodal set is a collection of $C^{1,α}$ hyper-surfaces (for every $0<α<1$), up to a residual set with small Hausdorff dimension. This result applies to the asymptotic limits of reaction-diffusion systems with strong competition interactions, to optimal partition problems involving eigenvalues, as well as to segregated standing waves for Bose-Einstein condensates in multiple hyperfine spin states.

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Hugo Tavares, Susanna Terracini. 2010-02-22. Regularity of the nodal set of segregated critical configurations under a weak reflection law. https://arxiv.org/abs/1002.3822

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