eprintid: 10185490 rev_number: 6 eprint_status: archive userid: 699 dir: disk0/10/18/54/90 datestamp: 2024-01-16 13:05:58 lastmod: 2024-01-16 13:05:58 status_changed: 2024-01-16 13:05:58 type: article metadata_visibility: show sword_depositor: 699 creators_name: Malagutti, Marcello title: Regularity and Semialgebraicity of Solutions of Linear EquationsSystems ispublished: pub divisions: UCL divisions: B04 divisions: C06 divisions: F59 keywords: Linear equations system, semialgebraic solution, Glaeser refinement, bundle section, semialgebraic set note: Copyright (c) 2024 Marcello Malagutti. This work is licensed under a Creative Commons Attribution 3.0 Unported License. abstract: This work is concerned with the study of a necessary and sufficient condition for the existence of solutions with a given regularity to a system of linear equations with coefficients of given regularity. First, to properly contextualize the subject matter and to introduce crucial analytical solving tools, we go through results by C.Fefferman- J.Kollár and by C.Fefferman - G.K.Luli. Then we prove our result to determine a necessary and sufficient condition for the existence of continuous (C0) semialgebraic solutions in case of a system of linear equations with continuous semialgebraic coefficients. date: 2024-01-09 date_type: published publisher: University of Bologna official_url: https://doi.org/10.6092/issn.2240-2829/18866 oa_status: green full_text_type: pub language: eng primo: open primo_central: open_green verified: verified_manual elements_id: 2139740 doi: 10.6092/issn.2240-2829/18866 lyricists_name: Malagutti, Marcello lyricists_id: MMALB52 actors_name: Malagutti, Marcello actors_id: MMALB52 actors_role: owner full_text_status: public publication: Bruno Pini Mathematical Analysis Seminar volume: 14 number: 2 pagerange: 201-228 issn: 2240-2829 citation: Malagutti, Marcello; (2024) Regularity and Semialgebraicity of Solutions of Linear EquationsSystems. Bruno Pini Mathematical Analysis Seminar , 14 (2) pp. 201-228. 10.6092/issn.2240-2829/18866 <https://doi.org/10.6092/issn.2240-2829%2F18866>. Green open access document_url: https://discovery.ucl.ac.uk/id/eprint/10185490/1/18866-Article%20Text-75011-1-10-20240102.pdf