发表机构
The University of Utah; University of California, Los Angeles（犹他大学; 加州大学洛杉矶分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究带缺陷的Bernoulli单相问题解的远场行为，建立了正常解在无穷远处的定量渐近展开，且对所有正常解一致成立。
AI 中文摘要
我们研究球外部区域中单相 Bernoulli 自由边界问题解的远场行为，以及具有单个紧支撑自由边界条件非均匀性（我们称之为缺陷）的整解。对于爆破后趋于半平面解的解（正常解），我们建立了无穷远处的渐近展开：在维度 $d \geq 3$ 中，自由边界高度以速率 $|x|^{2-d}$ 收敛到极限，并带有容量型系数；而在维度 $d=2$ 中，展开式包含对数项。一个重要的新颖之处在于，这些展开是定量的，并且对所有正常解一致成立。
英文摘要
We study the far-field behavior of solutions of the one-phase Bernoulli free boundary problem in the exterior of a ball, and of entire solutions with a single compactly supported inhomogeneity of the free boundary condition, which we call a defect. For solutions which blow down to a half-plane solution (proper solutions) we establish an asymptotic expansion at infinity: in dimension $d \geq 3$ the free boundary height converges to a limit at rate $|x|^{2-d}$ with a capacity-type coefficient, while in dimension $d=2$ the expansion carries a logarithmic term. A significant novelty is that the expansions are quantitative and uniform over all the proper solutions.
CommentsThis article was a part of the arXiv post arXiv:2512.11152v1, we have split that article into two parts. The companion article has already been posted as a replacement at arXiv:2512.11152v2, this posting serves as a replacement of the other half of arXiv:2512.11152
