%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.