{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001476028,0.0009661438,0.001046237,0.002299161,0.0009868494,0.002470018,0.001234975,0.001088531,0.002480285],"category_scores_gemma":[0.006938635,0.0005016078,0.0008348035,0.000669862,0.003297365,0.002461365,0.002218505,0.001669378,0.0002349556],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001023626,"about_ca_system_score_gemma":0.0007530205,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001442922,"about_ca_topic_score_gemma":0.001126807,"domain_scores_codex":[0.9995379,0.0001777622,0.00002591188,0.00006237339,0.0001180604,0.0000779631],"domain_scores_gemma":[0.9960127,0.002004099,0.0005966013,0.0001807235,0.0006393856,0.0005664297],"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":[0.0003495014,0.0001346038,0.002627414,0.0001285312,0.0000619749,0.0003866806,0.0006558485,0.05294689,0.01248211,0.9221984,0.001439467,0.006588655],"study_design_scores_gemma":[0.00004379977,0.00007440367,0.001752323,0.00002585138,0.00001093386,0.0001469607,0.0003452926,0.4517626,0.001598906,0.5433646,0.0008338846,0.00004044686],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7935602,0.0006210926,0.1827906,0.001475232,0.0001457791,0.00005914709,0.0001629985,0.0001135106,0.02107144],"genre_scores_gemma":[0.977877,0.000381865,0.009673777,0.00008977456,0.0001252779,0.00006440506,0.0001836699,0.00008622492,0.01151807],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.002480285,"threshold_uncertainty_score":0.008297443,"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."}}