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- W1990167075 abstract "Abstract Let F : = ( f 1 , … , f p ) : R n → R p be a polynomial map. This paper studies the existence of the following global Łojasiewicz-type inequality ‖ F ( x ) ‖ α + ‖ F ( x ) ‖ β ⩾ c d ( x , F − 1 ( 0 ) ) for all x ∈ R n , for some constants c > 0 , α > 0 , and β > 0 . We show that the above inequality holds if one of the following conditions is satisfied: (i) F is convenient and Khovanskii non-degenerate at infinity; (ii) F is convenient and non-degenerate at infinity; (iii) F is Mikhailov–Gindikin non-degenerate. Further, in cases (ii) and (iii), the exponents α and β can be determined explicitly." @default.
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- W1990167075 date "2014-02-01" @default.
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- W1990167075 title "Global Łojasiewicz-type inequality for non-degenerate polynomial maps" @default.
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- W1990167075 doi "https://doi.org/10.1016/j.jmaa.2013.08.044" @default.
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