[{"abstract":[{"lang":"eng","text":"I review recent contributions on nonlinear Dirichlet forms. Then, I specialise to the case of 2-\r\nhomogeneous and local forms. Inspired by the theory of Finsler manifolds and metric measure spaces, I establish new properties of such nonlinear Dirichlet forms, which are reminiscent of differential calculus formulae."}],"oa":1,"file":[{"creator":"dernst","date_created":"2026-05-18T08:26:15Z","file_name":"2026_LaMathematica_Brigati.pdf","file_id":"21892","content_type":"application/pdf","date_updated":"2026-05-18T08:26:15Z","success":1,"relation":"main_file","file_size":394082,"access_level":"open_access","checksum":"f75bffe3c793a2cbb26b8494024d0681"}],"month":"04","title":"Nonlinear Dirichlet forms, energy spaces, and calculus rules","date_published":"2026-04-29T00:00:00Z","article_type":"original","publication_identifier":{"eissn":["2730-9657"]},"date_updated":"2026-05-18T08:27:08Z","oa_version":"Published Version","type":"journal_article","publication_status":"published","file_date_updated":"2026-05-18T08:26:15Z","doi":"10.1007/s44007-026-00217-w","has_accepted_license":"1","PlanS_conform":"1","arxiv":1,"ddc":["510"],"status":"public","OA_type":"hybrid","publication":"La Matematica","quality_controlled":"1","citation":{"apa":"Brigati, G. (2026). Nonlinear Dirichlet forms, energy spaces, and calculus rules. <i>La Matematica</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s44007-026-00217-w\">https://doi.org/10.1007/s44007-026-00217-w</a>","short":"G. Brigati, La Matematica 5 (2026).","chicago":"Brigati, Giovanni. “Nonlinear Dirichlet Forms, Energy Spaces, and Calculus Rules.” <i>La Matematica</i>. Springer Nature, 2026. <a href=\"https://doi.org/10.1007/s44007-026-00217-w\">https://doi.org/10.1007/s44007-026-00217-w</a>.","ista":"Brigati G. 2026. Nonlinear Dirichlet forms, energy spaces, and calculus rules. La Matematica. 5(2), 33.","ama":"Brigati G. Nonlinear Dirichlet forms, energy spaces, and calculus rules. <i>La Matematica</i>. 2026;5(2). doi:<a href=\"https://doi.org/10.1007/s44007-026-00217-w\">10.1007/s44007-026-00217-w</a>","ieee":"G. Brigati, “Nonlinear Dirichlet forms, energy spaces, and calculus rules,” <i>La Matematica</i>, vol. 5, no. 2. Springer Nature, 2026.","mla":"Brigati, Giovanni. “Nonlinear Dirichlet Forms, Energy Spaces, and Calculus Rules.” <i>La Matematica</i>, vol. 5, no. 2, 33, Springer Nature, 2026, doi:<a href=\"https://doi.org/10.1007/s44007-026-00217-w\">10.1007/s44007-026-00217-w</a>."},"external_id":{"arxiv":["2309.00377"]},"department":[{"_id":"JaMa"}],"scopus_import":"1","article_processing_charge":"Yes (via OA deal)","intvolume":"         5","OA_place":"publisher","acknowledgement":"I am thankful to G. Savaré, for introducing me to the study of nonlinear Dirichlet forms and metric measure spaces, and to D. Manini for stimulating discussions. Open access funding provided by Institute of Science and Technology (IST Austria). The author has been funded by the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No 754362. Partial support has been obtained from the EFI ANR-17-CE40-0030 Project of the French National Research Agency.","language":[{"iso":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Springer Nature","year":"2026","issue":"2","article_number":"33","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"day":"29","corr_author":"1","date_created":"2026-05-17T22:02:10Z","author":[{"last_name":"Brigati","id":"63ff57e8-1fbb-11ee-88f2-f558ffc59cf1","full_name":"Brigati, Giovanni","first_name":"Giovanni"}],"_id":"21881","volume":5}]