{"paper":{"title":"Bounded imaginary powers of cone differential operators on higher order Mellin-Sobolev spaces and applications to the Cahn-Hilliard equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Elmar Schrohe, Nikolaos Roidos","submitted_at":"2013-11-19T11:31:32Z","abstract_excerpt":"Extending earlier results on the existence of bounded imaginary powers for cone differential operators on weighted $L^p$-spaces $\\mathcal{H}^{0,\\gamma}_p(\\mathbb{B})$ over a manifold with conical singularities, we show how the same assumptions also yield the existence of bounded imaginary powers on higher order Mellin-Sobolev spaces $\\mathcal{H}^{s,\\gamma}_p(\\mathbb{B})$, $s\\geq0$. As an application we then consider the Cahn-Hilliard equation on a manifold with (possibly warped) conical singularities. Relying on our work for the case of straight cones, we first establish $R$-sectoriality (and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.4702","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":""},"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"}