{"id":"W7116795971","doi":"10.1016/j.jde.2025.114035","title":"Sharp Hölder regularity of weak solutions of the Neumann problem and applications to nonlocal PDE in metric measure spaces","year":2025,"lang":"en","type":"article","venue":"Journal of Differential Equations","topic":"Fixed Point Theorems Analysis","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Cape Breton University","funders":"Natural Sciences and Engineering Research Council of Canada; Academy of Finland; National Science Foundation","keywords":"Measure (data warehouse); Metric (unit); Metric space; Neumann boundary condition; Weak solution; Measurable function","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":[0.00283826,0.001532245,0.001169603,0.001917548,0.0005559999,0.001495849,0.001397213,0.001653289,0.001176143],"category_scores_gemma":[0.01039658,0.0005034445,0.001424149,0.0006583103,0.002587881,0.003497333,0.003139354,0.002394264,0.0001645312],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0006512794,"about_ca_system_score_gemma":0.0003252045,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003664086,"about_ca_topic_score_gemma":0.0002669412,"domain_scores_codex":[0.9991818,0.0003238306,0.00004853798,0.0001715576,0.000175642,0.00009867067],"domain_scores_gemma":[0.9963935,0.001835335,0.0005559832,0.0002500035,0.0004644673,0.0005007613],"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":[0.000443824,0.0002087498,0.006464718,0.001036335,0.0002235453,0.0037958,0.001243027,0.07047857,0.09197392,0.7998809,0.002458531,0.02179211],"study_design_scores_gemma":[0.00004843542,0.0003695384,0.004153761,0.00007142675,0.00007279615,0.001070135,0.000307314,0.6515009,0.01308766,0.3261811,0.003058827,0.0000781534],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.361604,0.004536414,0.6167256,0.002982107,0.0005043951,0.000080003,0.0001723139,0.0001515659,0.01324361],"genre_scores_gemma":[0.9564661,0.002032724,0.03403148,0.0002577362,0.0005483203,0.00009249853,0.0001447241,0.00007900833,0.006347388],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.00283826,"threshold_uncertainty_score":0.0150103,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03285595607053091,"score_gpt":0.3015500754492126,"score_spread":0.2686941193786817,"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."}}