{"id":"W2001211398","doi":"10.1016/j.crma.2011.01.028","title":"Non-convex self-dual Lagrangians and variational principles for certain PDEʼs","year":2011,"lang":"en","type":"article","venue":"Comptes Rendus Mathématique","topic":"Nonlinear Partial Differential Equations","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"Queen's University","funders":"","keywords":"Mathematics; Partial differential equation; Boundary value problem; Calculus of variations; Applied mathematics; Pure mathematics; Mathematical analysis; Calculus (dental)","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":[0.0009193079,0.0003698813,0.0004132308,0.001117931,0.0006565462,0.001316318,0.0006509573,0.0006949201,0.001930881],"category_scores_gemma":[0.001481505,0.0002820397,0.00068913,0.0003533795,0.002275353,0.001684963,0.001460581,0.001291414,0.0002229078],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008702227,"about_ca_system_score_gemma":0.0007379914,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009766095,"about_ca_topic_score_gemma":0.0009989924,"domain_scores_codex":[0.9996762,0.00009927132,0.00001498147,0.00004669213,0.0001200709,0.00004271952],"domain_scores_gemma":[0.9995029,0.0001223246,0.0001107345,0.00003548053,0.0001117327,0.0001168156],"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":[0.000001803575,0.000007436827,0.0001069211,0.00001290091,0.000004161961,0.0000411197,0.00004993423,0.003966726,0.0005242484,0.9940919,0.000241154,0.0009516602],"study_design_scores_gemma":[0.00000809279,0.00001674937,0.0002519642,0.00001256463,0.00000334068,0.0001117485,0.00006497293,0.1235253,0.0003527733,0.8728437,0.002799235,0.000009557204],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2758932,0.001210965,0.6755221,0.002177043,0.0001888952,0.00007443529,0.0001621323,0.00008283853,0.04468846],"genre_scores_gemma":[0.8814891,0.0007962093,0.08972548,0.0003246147,0.000239582,0.0001013343,0.0002252662,0.00009890027,0.02699946],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.001930881,"threshold_uncertainty_score":0.006459475,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1023286125706846,"score_gpt":0.3081128142133967,"score_spread":0.2057842016427121,"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."}}