{"id":"W2004031622","doi":"10.1007/s00526-012-0582-4","title":"Regularity of semi-stable solutions to fourth order nonlinear eigenvalue problems on general domains","year":2012,"lang":"en","type":"article","venue":"Calculus of Variations and Partial Differential Equations","topic":"Nonlinear Partial Differential Equations","field":"Mathematics","cited_by":29,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of British Columbia","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Order (exchange); Combinatorics; Omega; Domain (mathematical analysis); Bounded function; Mathematics; Lambda; Eigenvalues and eigenvectors; Physics; Mathematical analysis; Quantum mechanics","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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0005366958,0.0003327875,0.0005881318,0.0003461794,0.0005088303,0.00005287164,0.0002343368,0.0002136071,0.0004760387],"category_scores_gemma":[0.001510491,0.0003176592,0.0002181172,0.0007865891,0.0001691438,0.000269944,0.0001929932,0.0002329949,0.00003717767],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000708485,"about_ca_system_score_gemma":0.0001808133,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003958966,"about_ca_topic_score_gemma":0.0002918216,"domain_scores_codex":[0.9969928,0.0003019075,0.00107253,0.0003725852,0.000586623,0.0006735499],"domain_scores_gemma":[0.997332,0.0006355087,0.0004183265,0.0006619743,0.0005321305,0.0004201054],"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":[0.00004565707,0.001891916,0.0001789697,0.000090861,0.0002094922,1.980508e-7,0.001943988,0.003343521,0.02500328,0.9664757,0.0002810668,0.0005353127],"study_design_scores_gemma":[0.002559054,0.0007064881,0.007650283,0.0002547979,0.001324698,0.000005340812,0.0002195728,0.9449297,0.02700858,0.01283132,0.001469961,0.001040205],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1690962,0.0000406709,0.828087,0.000356941,0.0004297309,0.000854564,0.0006513278,0.00006406102,0.0004195324],"genre_scores_gemma":[0.9755435,0.00001468486,0.02289899,0.00003505484,0.0005500527,0.0001211214,0.0002811655,0.00005154099,0.000503882],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.9536444,"threshold_uncertainty_score":0.9999275,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07338594235318817,"score_gpt":0.3211363703018077,"score_spread":0.2477504279486196,"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."}}