{"id":"W4385723858","doi":"10.1007/s12220-023-01400-z","title":"Existence of Solutions for Biharmonic Equations on Conical Singular Manifolds","year":2023,"lang":"en","type":"article","venue":"Journal of Geometric Analysis","topic":"Nonlinear Partial Differential Equations","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of British Columbia","funders":"Natural Sciences and Engineering Research Council of Canada; National Natural Science Foundation of China","keywords":"Mathematics; Cone (formal languages); Gravitational singularity; Sobolev space; Order (exchange); Conical surface; Combinatorics; Biharmonic equation; Exponent; Manifold (fluid mechanics); Space (punctuation); Mathematical analysis; Dirichlet problem; Pure mathematics; Geometry; Boundary value problem","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001269299,0.001443362,0.001359734,0.003698144,0.002058189,0.003451368,0.001618472,0.002462189,0.005422431],"category_scores_gemma":[0.00584276,0.000889331,0.001233993,0.0009523673,0.002730452,0.003462698,0.004543465,0.003553634,0.0006490833],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001831834,"about_ca_system_score_gemma":0.001168651,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00174951,"about_ca_topic_score_gemma":0.00132752,"domain_scores_codex":[0.999554,0.0001058658,0.00003290833,0.00006754797,0.0001188751,0.0001208412],"domain_scores_gemma":[0.9982108,0.0005526769,0.0002714701,0.00008325524,0.000400182,0.0004816577],"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":[0.0001084773,0.000112362,0.00109612,0.0001119098,0.00004769061,0.0003003327,0.0006781797,0.007875495,0.008431253,0.9731818,0.001791023,0.006265286],"study_design_scores_gemma":[0.00009028935,0.0001061049,0.001385662,0.0000892743,0.00003593566,0.0003674861,0.0011714,0.167088,0.002462904,0.824194,0.002930758,0.00007808096],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7709029,0.001637463,0.1704817,0.003963714,0.000501651,0.0001555859,0.0003705038,0.0002294515,0.05175703],"genre_scores_gemma":[0.9512283,0.0009254626,0.0214148,0.0003704261,0.000271171,0.0001210895,0.0004471414,0.0001214861,0.02510025],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.005422431,"threshold_uncertainty_score":0.0181399,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.2014936974982223,"score_gpt":0.3949172934859637,"score_spread":0.1934235959877414,"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."}}