{"paper":{"title":"Bifurcation of overdetermined capillary problems in a strip domain","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Pieralberto Sicbaldi, Yuanyuan Lian","submitted_at":"2026-06-18T07:44:21Z","abstract_excerpt":"In this paper, we consider the classical overdetermined capillary problem:\n  \\begin{equation*}\n  \\begin{cases}\n  \\mathrm{div} \\left(\\frac{\\nabla u}{\\sqrt{1+|\\nabla u|^2}}\\right) - bu =0 &~~\\mbox{in}~~ \\Omega,\n  \\partial_{\\nu} u=\\kappa &~~\\mbox{on}~~\\partial\\Omega,\n  u=c &~~\\mbox{on}~~\\partial\\Omega,\n  \\end{cases} \\end{equation*}\n  where $b$, $c$ and $\\kappa$ are positive constants, and $\\Omega\\subset \\mathbb{R}^2$. When $\\Omega$ is an infinite strip, i.e., a domain bounded by two parallel straight lines, there exists a unique one-dimensional solution (called the trivial solution) to this probl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.19885","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.19885/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}