{"id":"W2076998109","doi":"10.1142/s0218202501001240","title":"SOME MAXIMUM PRINCIPLES AND SYMMETRY RESULTS FOR A CLASS OF BOUNDARY VALUE PROBLEMS INVOLVING THE MONGE-AMPÈRE EQUATION","year":2001,"lang":"en","type":"article","venue":"Mathematical Models and Methods in Applied Sciences","topic":"Geometry and complex manifolds","field":"Mathematics","cited_by":12,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université Laval","funders":"","keywords":"Mathematics; Bounded function; Monge–Ampère equation; Domain (mathematical analysis); Boundary value problem; Symmetry (geometry); Maximum principle; Boundary (topology); Class (philosophy); Function (biology); Regular polygon; Mathematical analysis; Convex function; Combinatorics; Pure mathematics; Mathematical physics; Geometry; Mathematical optimization; Optimal control","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002592793,0.0006756693,0.001023619,0.0008564538,0.001511171,0.001795995,0.00133222,0.002178952,0.002845728],"category_scores_gemma":[0.003995507,0.0005656648,0.001472579,0.0004344211,0.002670311,0.003645117,0.001778596,0.001822754,0.0003925124],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007182416,"about_ca_system_score_gemma":0.0006744026,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003473058,"about_ca_topic_score_gemma":0.0001745483,"domain_scores_codex":[0.9993715,0.0002288347,0.00002779715,0.00007482847,0.0002029392,0.00009428727],"domain_scores_gemma":[0.9989298,0.0005824113,0.0001587369,0.0001092286,0.0001253825,0.00009439581],"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":[0.00002066046,0.00004636601,0.0004169232,0.00009732011,0.00001465682,0.0002258171,0.0002289695,0.01174163,0.003001734,0.9771827,0.0007574692,0.006265729],"study_design_scores_gemma":[0.00003082711,0.00005135003,0.000402205,0.00002606137,0.000006772709,0.0003270157,0.0001134917,0.08527391,0.001022386,0.9108903,0.00183316,0.00002233297],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.304744,0.003834162,0.6275328,0.003099117,0.0002508219,0.0001925956,0.0001183706,0.0001396169,0.06008855],"genre_scores_gemma":[0.8854232,0.002110884,0.0998702,0.0003549621,0.0004615703,0.0002420611,0.0001557565,0.0001329917,0.01124839],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.002845728,"threshold_uncertainty_score":0.01371211,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.2370585297486217,"score_gpt":0.397028352392807,"score_spread":0.1599698226441853,"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."}}