{"paper":{"title":"Hodge theory in the Sobolev topology for the de Rham complex","license":"","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Luigi Fontana, Marco M. Peloso, Steven G. Krantz","submitted_at":"1996-01-22T00:00:00Z","abstract_excerpt":"The authors study the Hodge theory of the exterior differential operator $d$ acting on $q$-forms on a smoothly bounded domain in $\\RR^{N+1}$, and on the half space $\\rnp$. The novelty is that the topology used is not an $L^2$ topology but a Sobolev topology. This strikingly alters the problem as compared to the classical setup. It gives rise to a boundary-value problem belonging to a class of problems first introduced by Vi\\v{s}ik and Eskin, and by Boutet de Monvel."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9601208","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":""},"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"}