Solutions of the Bernoulli one-phase problem with a defect

@misc{feldman2026solutions,
  title = {{Solutions of the Bernoulli one-phase problem with a defect}},
  author = {William M Feldman and Inwon C Kim},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.17066},
  eprint = {2609.17066},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.17066},
}

TY  - UNPB
TI  - Solutions of the Bernoulli one-phase problem with a defect
AU  - William M Feldman
AU  - Inwon C Kim
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2609.17066
UR  - https://arxiv.org/abs/2609.17066
AB  - 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 ≥ 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.
ER  -