%0 Journal Article %@ 2240-2829 %A Malagutti, Marcello %D 2024 %F discovery:10185490 %I University of Bologna %J Bruno Pini Mathematical Analysis Seminar %K Linear equations system, semialgebraic solution, Glaeser refinement, bundle section, semialgebraic set %N 2 %P 201-228 %T Regularity and Semialgebraicity of Solutions of Linear EquationsSystems %U https://discovery.ucl.ac.uk/id/eprint/10185490/ %V 14 %X 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. %Z Copyright (c) 2024 Marcello Malagutti. This work is licensed under a Creative Commons Attribution 3.0 Unported License.