Real Algebraic and Analytic Geometry
Submission: 2013, March 14.
In this paper, we give some Lojasiewicz-type inequalities and a nonsmooth slope inequality on non-compact domains for continuous definable functions in an o-minimal structure. We also give a necessary and sufficicent condition for which global error bound exists. Moreover, we point out the relationship between the Palais-Smale condition and this global error bound.
Mathematics Subject Classification (2000): 49K40; 32B20, 14P.
Keywords and Phrases: Lojasiewicz inequalities, error bounds, o-minimal structures.
Full text, 14p.: dvi 62k, pdf 316k.