{"paper":{"title":"Convexity of power functions and bilinear embedding for divergence-form operators with complex coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Andrea Carbonaro, Oliver Dragi\\v{c}evi\\'c","submitted_at":"2016-11-02T15:38:19Z","abstract_excerpt":"We introduce a condition on accretive matrix functions, called $p$-ellipticity, and discuss its applications to the $L^p$ theory of elliptic PDE with complex coefficients. Our examples are:\n  (i) generalized convexity of power functions (Bellman functions),\n  (ii) dimension-free bilinear embeddings,\n  (iii) $L^p$-contractivity of semigroups and\n  (iv) holomorphic functional calculus.\n  Recent work by Dindo\\v{s} and Pipher (arXiv:1612.01568v3) established close ties between $p$-ellipticity and\n  (v) regularity theory of elliptic PDE with complex coefficients.\n  The $p$-ellipticity condition ari"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.00653","kind":"arxiv","version":4},"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"}