发表机构
The University of Western Australia; Università della Calabria（西澳大利亚大学; 卡塔尼亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究Robin型非局部非线性泛函的自由最小化问题，证明极小元存在唯一并具衰减性，分析参数映射的正则性，并给出能量在参数趋于无穷和零时的渐近展开，揭示零质量情形下的发散行为。
AI 中文摘要
我们研究了一个与依赖于正参数$\alpha$的Robin型非局部外部条件相关的非线性、非局部泛函的自由最小化问题。我们证明了对于每个$\alpha>0$，极小元存在且唯一，并在无穷远处满足适当的衰减性质。我们还研究了映射$\alpha \mapsto u_\alpha$和$\alpha \mapsto E_\alpha$的正则性，其中$u_\alpha$表示极小元，$E_\alpha$表示相应的能量。最后，我们推导了当$\alpha\to+\infty$和$\alpha\to0^+$时能量的渐近展开。后一种情形需要根据强迫项是否具有零质量来区分两种情况。在一种情况下，极限能量具有极小元且$E_\alpha$收敛到其能量，但在另一种情况下，$E_\alpha$发散到$-\infty$。
英文摘要
We study the free minimization problem for a nonlinear, nonlocal functional associated with Robin-type nonlocal exterior conditions depending on a positive parameter $α$. We prove that, for every $α>0$, the minimizer exists, is unique, and satisfies suitable decay properties at infinity. We also investigate the regularity of the maps $α\mapsto u_α$ and $α\mapsto E_α$, where~$u_α$ denotes the minimizer and $E_α$ the corresponding energy. Finally, we derive asymptotic expansions of the energy as $α\to+\infty$ and as $α\to0^+$. The latter regime requires distinguishing between two cases, depending on whether the forcing term has zero mass. In one case, the limiting energy possesses a minimizer and $E_α$ converges to its energy, but in the other case $E_α$ diverges to $-\infty$.
Comments22 pages
