Bộ môn Giải tích

We give some versions of Lojasiewicz inequalities on non-compact sets for some polynomial and semialgebraic functions with explicit exponents. More precisely, we give some necessary and sufficient conditions for which Lojasiewicz inequalities exists on some domains which are not compact. Moreover, under some conditions of non-degeneracy at infinity, all the Lojasiewicz exponents can be estimated.