{"id":"W4213192483","doi":"10.28924/2291-8639-20-2022-13","title":"An Extension of a Variational Inequality in the Simader Theorem to a Variable Exponent Sobolev Space and Applications: The Dirichlet Case","year":2022,"lang":"en","type":"article","venue":"International Journal of Analysis and Applications","topic":"Nonlinear Partial Differential Equations","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Standard probability space; Sobolev inequality; Sobolev space; Exponent; Mathematical analysis; Lp space; Space (punctuation); Variable (mathematics); Extension (predicate logic); Dirichlet distribution; Pure mathematics; Dirichlet problem; Lebesgue integration; Boundary value problem; Banach space","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002375297,0.0008688694,0.0007763914,0.00168847,0.0009845438,0.001307333,0.001147726,0.001405258,0.002978055],"category_scores_gemma":[0.004847406,0.0003136239,0.00131544,0.0007484847,0.002409074,0.003951682,0.003813423,0.003692383,0.0003467339],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008933026,"about_ca_system_score_gemma":0.0007384518,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001054892,"about_ca_topic_score_gemma":0.000926061,"domain_scores_codex":[0.999163,0.0003263671,0.00003751072,0.0001791328,0.0001962498,0.00009765955],"domain_scores_gemma":[0.998288,0.0008750421,0.0001624404,0.0001011441,0.0003529757,0.0002203672],"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":[0.00003476373,0.00003380179,0.0005142035,0.0001540362,0.00001967713,0.0002649375,0.0001935352,0.00588929,0.006101051,0.9675187,0.001414094,0.0178619],"study_design_scores_gemma":[0.00001802734,0.0001610654,0.0009184814,0.0001048209,0.00002536774,0.0004937467,0.0001388632,0.1679516,0.004085606,0.8064882,0.01956804,0.00004616974],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.05962931,0.005617071,0.8723594,0.005403827,0.001350869,0.00005669732,0.0001617078,0.00006221409,0.05535891],"genre_scores_gemma":[0.7702579,0.007040908,0.1844653,0.00195761,0.002613141,0.000193143,0.0002475489,0.0001779437,0.03304648],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.002978055,"threshold_uncertainty_score":0.01256186,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03737293162096418,"score_gpt":0.3637060705004349,"score_spread":0.3263331388794707,"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."}}