AI 中文总结
该研究针对含p-拉普拉斯算子的玻色-爱因斯坦凝聚系统的异宿解，通过建立其渐近行为、单调性等性质，推导了势阱附近的曲率估计，为构造径向障碍函数提供几何控制。
AI 中文摘要
我们研究涉及p-拉普拉斯算子的向量值玻色-爱因斯坦凝聚系统的异宿解。主要困难来自p-拉普拉斯算子的退化性以及势阱可能存在的非光滑行为。在对双阱势作出适当假设下，我们建立了异宿解的存在性及详细渐近行为，特别证明了每个分量的严格单调性，通过Weiss型单调性公式对势阱附近的爆破轮廓进行分类，并得到解的几乎齐次性。此外，在通过l_p弧长对异宿解重新参数化后，我们推导出轨迹在势阱附近的曲率估计，这些结果为对应玻色-爱因斯坦凝聚系统径向障碍函数的构造提供了所需的几何控制。
英文摘要
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.
