{"id":"W2016275009","doi":"10.3934/dcdsb.2009.11.145","title":"$L^p$-integrability & weak type $L^{2}$-estimates for the gradient of harmonic mappings of $\\mathbb D$","year":2008,"lang":"en","type":"article","venue":"Discrete and Continuous Dynamical Systems - B","topic":"Advanced Harmonic Analysis Research","field":"Mathematics","cited_by":9,"is_retracted":false,"has_abstract":true,"ca_institutions":"Toronto Metropolitan University","funders":"","keywords":"Mathematics; Type (biology); Homeomorphism (graph theory); Harmonic; Extension (predicate logic); Elementary proof; Pure mathematics; Harmonic function; Mathematical analysis; Mathematical physics; Combinatorics; Physics; Quantum mechanics; Computer science","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0006665994,0.0002136024,0.0007994709,0.00006700739,0.0001642009,0.00001904253,0.0003400275,0.0001067395,0.00001974339],"category_scores_gemma":[0.001074691,0.0001324097,0.0002548923,0.0002404184,0.0005372271,0.00006551341,0.0001180154,0.0001904408,0.000002843614],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005458729,"about_ca_system_score_gemma":0.00005677671,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004870512,"about_ca_topic_score_gemma":0.00006642117,"domain_scores_codex":[0.9980433,0.0001021799,0.0007664014,0.0003326016,0.0003916638,0.000363837],"domain_scores_gemma":[0.9970102,0.001565912,0.0003579249,0.0005669683,0.0003985679,0.0001004371],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.002155324,0.001202883,0.04730192,0.006545809,0.003652399,0.00001679145,0.006120847,0.0002571509,0.04426858,0.8762634,0.005431597,0.006783247],"study_design_scores_gemma":[0.008798731,0.002566105,0.03646884,0.002377753,0.002853406,0.000451088,0.01226887,0.7071908,0.003584554,0.1912632,0.02940094,0.002775667],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8446729,0.002442,0.1507213,0.0001785276,0.0001045336,0.001214726,0.00009684085,0.00005003008,0.0005191073],"genre_scores_gemma":[0.9958131,0.0001615313,0.002328519,0.0000045459,0.00002970392,0.00009167517,0.00001968528,0.00002789499,0.001523347],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.7069337,"threshold_uncertainty_score":0.5399509,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05946511273569983,"score_gpt":0.3334910311433645,"score_spread":0.2740259184076647,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}