A density result for homogeneous Sobolev spaces on planar domains

2018/01/09 by Nandi, Debanjan, Rajala, Tapio, Schultz, Timo · 1 citation
#46E35 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1801.02824

Abstract

We show that in a bounded simply connected planar domain Ω the smooth Sobolev functions W^k,∞(Ω)∩ C^∞(Ω) are dense in the homogeneous Sobolev spaces L^k,p(Ω).

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• Density problem for Sobolev spaces on Gehring Hayman domains with the ball separation condition in metric measure spaces

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