{"paper":{"title":"Homogenization and operator estimates for Steklov problems in perforated domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Andrii Khrabustovskyi, Jari Taskinen","submitted_at":"2026-03-26T06:59:16Z","abstract_excerpt":"Let the set $\\Omega_\\varepsilon$ be obtained from the bounded domain $\\Omega$ by removing a family of $\\varepsilon$-periodically distributed identical balls. In $\\Omega_\\varepsilon$ one considers the Steklov spectral problem. It is known from [Girouard-Henrot-Lagac\\'e, ARMA (2021)] that, if the radii of the holes shrink at a critical rate such that the surface area of a single hole is comparable to the volume of a periodicity cell, then, in the limit $\\varepsilon \\to 0$, the Steklov spectrum converges to the spectrum of the problem $-\\Delta u=\\lambda Q u$ on $\\Omega$ with some weight $Q>0$. In"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.25094","kind":"arxiv","version":2},"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/2603.25094/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"}