Real Algebraic and Analytic Geometry
Submission: 2008, January 15.
A John function is a continuously differentiable function whose gradient is bounded by the reciprocal of the Euclidean distance to the boundary of the domain. Here we construct John functions whose gradient norms have positive lower bounds for o-minimal domains. We prove their definability and give explicit estimates for number of John functions required for a given set to obtain uniform positive lower bounds.
Mathematics Subject Classification (2000): 26B99,14P10,14P15,03C64.
Keywords and Phrases: John functions, o-minimal structures.
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