Regularity and Semialgebraicity of Solutions of Linear Equations Systems

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.