Poincaré inequality on subanalytic sets

2020/10/22 by Valette, Anna, Valette, Guillaume · 1 citation
#14P10 #26D10 #32B20 #Algebraic Geometry (math.AG) #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2010.11529

Abstract

Let Ω be a subanalytic bounded open subset of ℝⁿ, with possibly singular boundary. We show that given p∈ [1,∞), there is a constant C such that for any u∈ W^1,p(Ω) we have ||u-u_Ω||_L^p ≤ C||∇ u||_L^p, where we have set u_Ω:=(1)/(|Ω|)∫_Ω u.

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• W^1,p priori estimates for solutions of linear elliptic PDEs on subanalytic domains

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