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.
Malagutti, M. (2023). REGULARITY AND SEMIALGEBRAICITY OF SOLUTIONS OF LINEAR EQUATIONS SYSTEMS. BRUNO PINI MATHEMATICAL ANALYSIS SEMINAR, 14(2), 201-228 [10.6092/issn.2240-2829/18866].
REGULARITY AND SEMIALGEBRAICITY OF SOLUTIONS OF LINEAR EQUATIONS SYSTEMS
Malagutti M.Primo
2023
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.| File | Dimensione | Formato | |
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