{"id":"W4386136352","doi":"10.1515/jaa-2023-0031","title":"Korn’s inequality in anisotropic Sobolev spaces","year":2023,"lang":"en","type":"article","venue":"Journal of Applied Analysis","topic":"Nonlinear Partial Differential Equations","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Saskatchewan","funders":"","keywords":"Mathematics; Sobolev inequality; Inequality; Kantorovich inequality; Sobolev space; Extension (predicate logic); Pure mathematics; Rearrangement inequality; Hölder's inequality; Anisotropy; Linear inequality; Log sum inequality; Poincaré inequality; Interpolation space; Mathematical analysis; Functional analysis; Computer science","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0008121266,0.0001156637,0.0005593181,0.0009945078,0.00004587809,0.00005000598,0.0002063496,0.00006714139,0.0001969648],"category_scores_gemma":[0.0002275986,0.00009595817,0.0003157519,0.002619202,0.00002825608,0.00007366596,0.00004998984,0.0002142798,0.00006927814],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006452828,"about_ca_system_score_gemma":0.00005588151,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000321073,"about_ca_topic_score_gemma":0.0005124648,"domain_scores_codex":[0.9983885,0.00007085098,0.0007711318,0.0001252679,0.000440849,0.0002034062],"domain_scores_gemma":[0.9987924,0.0002957809,0.0004949511,0.0002271152,0.0001043964,0.00008537131],"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":[0.0008777445,0.003790856,0.1789254,0.0006124316,0.01728451,0.0004658526,0.01580135,0.06589202,0.07144225,0.6100097,0.00942976,0.0254682],"study_design_scores_gemma":[0.002962237,0.000175155,0.1956115,0.00008040514,0.005941956,0.000005633657,0.00415091,0.03797498,0.005718019,0.7455376,0.001118595,0.0007229518],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9872929,0.00001063089,0.01114402,0.0003927544,0.00005900698,0.00006835697,0.000007740777,0.00003102134,0.000993578],"genre_scores_gemma":[0.9944882,0.00002695092,0.005161802,0.00002632065,0.000171245,0.000003875882,0.000008158327,0.00001327463,0.0001001134],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1355279,"threshold_uncertainty_score":0.391306,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06873157303586798,"score_gpt":0.3591620246903485,"score_spread":0.2904304516544805,"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."}}