2018/12/12 by Beata Osińska-Ulrych, Osińska-Ulrych, Beata, Grzegorz Skalski +3
Computer Science · Mathematics · #11E25 #14P05 #14R99 #32S70 #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematical Inequalities and Applications #Nonlinear Differential Equations Analysis #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.1812.04883
openalex publication_date 2018/12/12 · openalex created_date 2022/08/01 · openalex updated_date 2026/07/28
Let X⊂ ℝn be a compact semialgebraic set and let f:X→ ℝ be a nonzero Nash function. We give a Solernó and D'Acunto-Kurdyka type estimation of the exponent \varrho∈[0,1) in the Łojasiewicz gradient inequality |∇ f(x)|≥ C|f(x)|^\varrho for x∈ X, |f(x)|0, in terms of the degree of a polynomial P such that P(x,f(x))=0, x∈ X. As a corollary we obtain an estimation of the degree of sufficiency of non-isolated Nash functions singularities