arXiv:2611.08670v1 Announce Type: new 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).
Continue to arXiv Mathematics →You are being forwarded in 6s — stay on this page