Curvature estimate for the heteroclinical solution to a Bose-Einstein condensation system

Leyun Wu; Chilin Zhang

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arXiv · 2608.09760

Curvature estimate for the heteroclinical solution to a Bose-Einstein condensation system

Leyun Wu·Chilin Zhang

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Abstract

We investigate heteroclinical solutions of a vector-valued Bose-Einstein condensation system involving the $p$-Laplacian. The main difficulty comes from the degeneracy of the $p$-Laplacian and the possible nonsmooth behavior of the potential wells. Under suitable assumptions on the double-well potential, we establish the existence and detailed asymptotic behavior of heteroclinical solutions. In particular, we prove the strict monotonicity of every component, classify the blow-up profiles near the potential wells through Weiss-type monotonicity formulas, and obtain an almost homogeneity property of the solution. Furthermore, after re-parametrizing the heteroclinical solution by its $l_p$-arc length, we derive a curvature estimate for the trajectory near the potential wells. These results provide the geometric control needed for the construction of radial barrier functions for the corresponding Bose-Einstein condensation system.

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Leyun Wu, Chilin Zhang. 2026-08-10. Curvature estimate for the heteroclinical solution to a Bose-Einstein condensation system. https://arxiv.org/abs/2608.09760

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