D. Kinzebulatov, Department of Mathematics, University of Toronto, Toronto, Ontario M5S 2E4; email: dkinzl@math.toronto.edu

L. Shartser, Department of Mathematics, University of Toronto, Toronto, Ontario M5S 2E4; email: shartl@math.toronto.edu

Abstract/Résumé:

Given an analytic set \(X\) and \(x \in X\), we show that \(X\) admits (in a relatively compact neighbourhood of \(x\)) a modified Gagliardo–Nirenberg inequality, depending on a certain exponent \(s \geq 1\) (\(s=1\) in case of a manifold). The infimum of the set of all such \(s\) characterizes, in a sense, the type of singularity at \(x\).

Etant donné un ensemble analytique \(X\) et \(x \in X\), nous montrons que \(X\) admet (dans un voisinage relativement compact de \(x\)) une inégalité de Gagliardo–Nirenberg modifiée, en fonction d’un certain exposant \(s \geq 1\) (\(s=1\) dans le cas d’une variété). La borne inférieure de l’ensemble de tous ces \(s\) caractérise, en un sens, le type de singularité en \(x\).

Keywords: Gaglardo–Nirenberg inequality, analytic sets, resolution of singularities

AMS Subject Classification: Local singularities 32S05

PDF(click to download): A note on Gagliardo--Nirenberg type inequalities on analytic sets