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- W986361880 abstract "Spectral matters form a powerful motivation for the study of these inequalities. Thus let Ω be an open subset of Rn with volume |Ω| and let Δ D,Ω ,Δ N,Ω be respectively the Dirichlet Laplacian and the Neumann Laplacian on Ω. We recall that —Δ D,Ω is the Friedrichs extension of -Δ on C ∞ 0(Ω) and that its domain D(—Δ D,Ω )is contained in the Sobolev space W 1 2(Ω): v is the Dirichlet Laplacian of u ∈ D(—Δ D,Ω ), v = Δu, if it belongs to L 1, 1oc (Ω) and for all φ ∈ C ∞ 0(Ω), $$ intlimits_Omega {nabla u.nabla emptyset dx = - intlimits_Omega upsilon } emptyset dx. $$ KeywordsOrlicz SpaceHardy InequalityContinuous NormBanach Function SpaceYoung FunctionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves." @default.
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- W986361880 date "2004-01-01" @default.
- W986361880 modified "2023-09-24" @default.
- W986361880 title "Poincaré and Hardy inequalities" @default.
- W986361880 doi "https://doi.org/10.1007/978-3-662-07731-3_4" @default.
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