{"paper":{"title":"Behaviour of solutions to $p$-Laplacian with Robin boundary conditions as $p$ goes to $1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Francescantonio Oliva, Francesco Della Pietra, Sergio Segura de Le\\'on","submitted_at":"2022-06-07T14:21:08Z","abstract_excerpt":"We study the asymptotic behaviour, as $p\\to 1^{+}$, of the solutions of the following inhomogeneous Robin boundary value problem: \\begin{equation} \\label{pbabstract} \\tag{P}\n  \\left\\{\\begin{array}{ll}\n  \\displaystyle -\\Delta_p u_p = f & \\text{in }\\Omega,\n  \\displaystyle |\\nabla u_p|^{p-2}\\nabla u_p\\cdot \\nu +\\lambda |u_p|^{p-2}u_p = g& \\text{on } \\partial\\Omega,\n  \\end{array}\\right. \\end{equation} where $\\Omega$ is a bounded domain in $\\mathbb R^{N}$ with sufficiently smooth boundary, $\\nu$ is its unit outward normal vector and $\\Delta_p v$ is the $p$-Laplacian operator with $p>1$. The data $f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.03337","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/2206.03337/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"}