6533b83afe1ef96bd12a7102
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A Density Result for Homogeneous Sobolev Spaces on Planar Domains
Tapio RajalaDebanjan NandiTimo Schultzsubject
Pure mathematicsMathematics::Analysis of PDEs01 natural sciencesPotential theoryDomain (mathematical analysis)010104 statistics & probabilityPlanartiheysSimply connected spaceClassical Analysis and ODEs (math.CA)FOS: Mathematics46E350101 mathematicsMathematicsMathematics::Functional AnalysisFunctional analysis010102 general mathematicshomogeneous Sobolev spaceSobolev spaceFunctional Analysis (math.FA)Sobolev spaceMathematics - Functional AnalysisHomogeneousMathematics - Classical Analysis and ODEsBounded functionAnalysisdescription
We show that in a bounded simply connected planar domain $\Omega$ the smooth Sobolev functions $W^{k,\infty}(\Omega)\cap C^\infty(\Omega)$ are dense in the homogeneous Sobolev spaces $L^{k,p}(\Omega)$.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2018-01-09 |