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PreprintarXiv licencearXiv

Non-conical classical solutions to the one-phase free boundary problem with an isolated singularity

  • Minyoung Jeong
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Abstract

Several examples of one-homogeneous classical solutions to the one-phase free boundary problem with an isolated free boundary singularity are known. Adapting the approach of Caffarelli, Hardt, and Simon for minimal surfaces, we construct non-conical classical solutions with an isolated free boundary singularity by perturbing a one-homogeneous solution U. Moreover, if U is strictly stable (respectively, non-degenerate), then any solution sufficiently close to U is also strictly stable (respectively, non-degenerate).

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Cite

BibTeXRIS
BibTeX
@misc{jeong2026nonconical,
  title = {{Non-conical classical solutions to the one-phase free boundary problem with an isolated singularity}},
  author = {Minyoung Jeong},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.08670},
  eprint = {2611.08670},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.08670},
}
RIS
TY  - UNPB
TI  - Non-conical classical solutions to the one-phase free boundary problem with an isolated singularity
AU  - Minyoung Jeong
PY  - 2026
DA  - 2026/11/05
PB  - arXiv
DO  - 10.48550/arxiv.2611.08670
UR  - https://arxiv.org/abs/2611.08670
AB  - Several examples of one-homogeneous classical solutions to the one-phase free boundary problem with an isolated free boundary singularity are known. Adapting the approach of Caffarelli, Hardt, and Simon for minimal surfaces, we construct non-conical classical solutions with an isolated free boundary singularity by perturbing a one-homogeneous solution U. Moreover, if U is strictly stable (respectively, non-degenerate), then any solution sufficiently close to U is also strictly stable (respectively, non-degenerate).
ER  -