{"id":"W2954608842","doi":"10.1016/j.aim.2019.06.020","title":"Existence and nonexistence of extremal functions for sharp Trudinger-Moser inequalities","year":2019,"lang":"en","type":"article","venue":"Advances in Mathematics","topic":"Nonlinear Partial Differential Equations","field":"Mathematics","cited_by":40,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of British Columbia","funders":"National Science Foundation","keywords":"Mathematics; Infimum and supremum; Type (biology); Inequality; Symmetry (geometry); Pure mathematics; Euler's formula; Function (biology); Space (punctuation); Mathematical analysis; Geometry","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":[0.0003613101,0.0001642783,0.0004178848,0.0001078004,0.00004737976,0.00001974222,0.0001670795,0.00006592149,0.0001076521],"category_scores_gemma":[0.0008790942,0.0001497904,0.00007267653,0.0001805223,0.0001118246,0.0002974529,0.00006863305,0.00009800815,0.00001663417],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002654274,"about_ca_system_score_gemma":0.00002848246,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000003895074,"about_ca_topic_score_gemma":0.00009276257,"domain_scores_codex":[0.9986784,0.00003235144,0.0006188921,0.0002256267,0.0002172295,0.0002274437],"domain_scores_gemma":[0.997565,0.001648332,0.0002875856,0.0003487311,0.0001084757,0.00004190671],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00003229942,0.0003224007,0.001746677,0.002557639,0.00002234933,5.893625e-7,0.002831657,0.0000376428,0.001635071,0.9888288,0.000021098,0.001963812],"study_design_scores_gemma":[0.0007572997,0.0001567566,0.0002942802,0.0005188456,0.00005304766,0.00000598487,0.003026495,0.0134695,0.001541946,0.9790953,0.0008179032,0.0002625848],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8762863,0.0007261843,0.1104804,0.00008250384,0.0003634712,0.001277665,0.0001353988,0.00007585603,0.01057223],"genre_scores_gemma":[0.6404791,0.0001298964,0.3564928,0.00001668735,0.00006480453,0.0001369896,0.00001310133,0.00004105847,0.002625545],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2460123,"threshold_uncertainty_score":0.6108276,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07632475994928917,"score_gpt":0.3655227092826624,"score_spread":0.2891979493333732,"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."}}