[{"language":[{"iso":"eng"}],"article_type":"original","doi":"10.1007/s11118-025-10251-y","project":[{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"},{"grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics"},{"grant_number":"ESP156_N","_id":"34c6ea2d-11ca-11ed-8bc3-c04f3c502833","name":"Gradient flow techniques for quantum Markov semigroups"}],"oa":1,"researchdata_availability":"no","external_id":{"arxiv":["2301.01035"]},"month":"01","issue":"1","das_tickbox":"1","status":"public","date_created":"2025-12-14T23:02:03Z","publication_identifier":{"eissn":["1572-929X"],"issn":["0926-2601"]},"mathsc":["31C15","31C25","35A15","35J10","47D07"],"supplementarymaterial":"no","file":[{"file_id":"22414","success":1,"creator":"dernst","file_size":445935,"checksum":"9f5a4e900b8d4c74c6b5bf7c3bad54e1","content_type":"application/pdf","date_updated":"2026-07-27T10:25:21Z","relation":"main_file","access_level":"open_access","file_name":"2026_PotentialAnalysis_Keller.pdf","date_created":"2026-07-27T10:25:21Z"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","keyword":["Dirichlet forms","Domination of semigroups","Dirichlet","Neumann and Robin boundary conditions"],"file_date_updated":"2026-07-27T10:25:21Z","citation":{"apa":"Keller, M., Lenz, D., Schmidt, M., Schwarz, M., &#38; Wirth, M. (2026). Boundary representations of intermediate forms between a regular Dirichlet form and its active main part. <i>Potential Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11118-025-10251-y\">https://doi.org/10.1007/s11118-025-10251-y</a>","ieee":"M. Keller, D. Lenz, M. Schmidt, M. Schwarz, and M. Wirth, “Boundary representations of intermediate forms between a regular Dirichlet form and its active main part,” <i>Potential Analysis</i>, vol. 64, no. 1. Springer Nature, 2026.","short":"M. Keller, D. Lenz, M. Schmidt, M. Schwarz, M. Wirth, Potential Analysis 64 (2026).","mla":"Keller, Matthias, et al. “Boundary Representations of Intermediate Forms between a Regular Dirichlet Form and Its Active Main Part.” <i>Potential Analysis</i>, vol. 64, no. 1, 6, Springer Nature, 2026, doi:<a href=\"https://doi.org/10.1007/s11118-025-10251-y\">10.1007/s11118-025-10251-y</a>.","chicago":"Keller, Matthias, Daniel Lenz, Marcel Schmidt, Michael Schwarz, and Melchior Wirth. “Boundary Representations of Intermediate Forms between a Regular Dirichlet Form and Its Active Main Part.” <i>Potential Analysis</i>. Springer Nature, 2026. <a href=\"https://doi.org/10.1007/s11118-025-10251-y\">https://doi.org/10.1007/s11118-025-10251-y</a>.","ama":"Keller M, Lenz D, Schmidt M, Schwarz M, Wirth M. Boundary representations of intermediate forms between a regular Dirichlet form and its active main part. <i>Potential Analysis</i>. 2026;64(1). doi:<a href=\"https://doi.org/10.1007/s11118-025-10251-y\">10.1007/s11118-025-10251-y</a>","ista":"Keller M, Lenz D, Schmidt M, Schwarz M, Wirth M. 2026. Boundary representations of intermediate forms between a regular Dirichlet form and its active main part. Potential Analysis. 64(1), 6."},"ec_funded":1,"day":"01","oa_version":"Published Version","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"OA_type":"hybrid","publication_status":"published","_id":"20814","article_number":"6","fulldoi":"https://doi.org/10.1007/s11118-025-10251-y","title":"Boundary representations of intermediate forms between a regular Dirichlet form and its active main part","publisher":"Springer Nature","intvolume":"        64","abstract":[{"lang":"eng","text":"We characterize all semigroups sandwiched between the semigroup of a Dirichlet form and the semigroup of its active main part. In case the Dirichlet form is regular, we give a more explicit description of the quadratic forms of the sandwiched semigroups in terms of pairs consisting of an open set and a measure on an abstract boundary."}],"has_accepted_license":"1","quality_controlled":"1","ddc":["510"],"publication":"Potential Analysis","date_published":"2026-01-01T00:00:00Z","OA_place":"publisher","PlanS_conform":"1","arxiv":1,"acknowledgement":"Open Access funding enabled and organized by Projekt DEAL. The first three authors acknowledge financial support of the DFG within the priority programme Geometry at Infinity.\r\nM.W. acknowledges financial support by the German Academic Scholarship Foundation, by the Austrian Science Fund (FWF) through grant number F65 and the Esprit Programme [ESP 156], and by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 716117).","article_processing_charge":"Yes (via OA deal)","author":[{"last_name":"Keller","first_name":"Matthias","full_name":"Keller, Matthias"},{"last_name":"Lenz","first_name":"Daniel","full_name":"Lenz, Daniel"},{"last_name":"Schmidt","first_name":"Marcel","full_name":"Schmidt, Marcel"},{"last_name":"Schwarz","full_name":"Schwarz, Michael","first_name":"Michael"},{"id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","last_name":"Wirth","orcid":"0000-0002-0519-4241","first_name":"Melchior","full_name":"Wirth, Melchior"}],"dataavailabilitystatement":"No datasets were generated or analysed during the current study.","date_updated":"2026-07-27T10:25:46Z","year":"2026","department":[{"_id":"JaMa"}],"volume":64,"type":"journal_article","scopus_import":"1"}]