{"paper":{"title":"A Counterexample to Kenig's Interpolation Problem for Sobolev Spaces with Zero Boundary Conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.FA"],"primary_cat":"math.AP","authors_text":"Dachun Yang, Sibei Yang, Wen Yuan, Xiaosheng Lin, Yangyang Zhang","submitted_at":"2026-05-26T14:54:34Z","abstract_excerpt":"Let $n\\in \\mathbb N\\cap[2,\\infty)$. In this article, we show that there exists a bounded $C^1$ domain $\\Omega\\subset \\mathbb R^n$ such that, for any given $s\\in(1,2)\\setminus\\{\\frac32\\}$, \\begin{align*} \\left[H_0^1(\\Omega),H^2(\\Omega)\\cap H_0^1(\\Omega)\\right]_{s-1} =H^s(\\Omega)\\cap H_0^1(\\Omega)=H_0^s(\\Omega) \\end{align*} with equivalent norms, but \\begin{align*} \\left[H_0^1(\\Omega),H^2(\\Omega)\\cap H_0^1(\\Omega)\\right]_{\\frac12} \\subsetneqq H^{\\frac32}(\\Omega)\\cap H_0^1(\\Omega), \\end{align*} which provides a counterexample to Problem 3.3.19 of Kenig in [CBMS Regional Conf. Ser. in Math. 83, 19"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.27119","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/2605.27119/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"}