@article{discovery10185490, publisher = {University of Bologna}, volume = {14}, month = {January}, pages = {201--228}, note = {Copyright (c) 2024 Marcello Malagutti. This work is licensed under a Creative Commons Attribution 3.0 Unported License.}, title = {Regularity and Semialgebraicity of Solutions of Linear EquationsSystems}, year = {2024}, journal = {Bruno Pini Mathematical Analysis Seminar}, number = {2}, author = {Malagutti, Marcello}, 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.Koll{\'a}r 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.}, url = {https://doi.org/10.6092/issn.2240-2829/18866}, keywords = {Linear equations system, semialgebraic solution, Glaeser refinement, bundle section, semialgebraic set}, issn = {2240-2829} }