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- W2896482971 abstract "Abstract We consider different fractional Neumann Laplacians of order <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>s</m:mi> <m:mo>∈</m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mn>0</m:mn> <m:mo>,</m:mo> <m:mn>1</m:mn> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> </m:math> {sin(0,1)} on domains <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi mathvariant=normal>Ω</m:mi> <m:mo>⊂</m:mo> <m:msup> <m:mi>ℝ</m:mi> <m:mi>n</m:mi> </m:msup> </m:mrow> </m:math> {Omegasubsetmathbb{R}^{n}} , namely, the restricted Neumann Laplacian <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msubsup> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mrow> <m:mo>-</m:mo> <m:msubsup> <m:mi mathvariant=normal>Δ</m:mi> <m:mi mathvariant=normal>Ω</m:mi> <m:mi>N</m:mi> </m:msubsup> </m:mrow> <m:mo stretchy=false>)</m:mo> </m:mrow> <m:mi mathvariant=normal>R</m:mi> <m:mi>s</m:mi> </m:msubsup> </m:math> {{(-Delta_{Omega}^{N})^{s}_{mathrm{R}}}} , the semirestricted Neumann Laplacian <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msubsup> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mrow> <m:mo>-</m:mo> <m:msubsup> <m:mi mathvariant=normal>Δ</m:mi> <m:mi mathvariant=normal>Ω</m:mi> <m:mi>N</m:mi> </m:msubsup> </m:mrow> <m:mo stretchy=false>)</m:mo> </m:mrow> <m:mi>Sr</m:mi> <m:mi>s</m:mi> </m:msubsup> </m:math> {{(-Delta_{Omega}^{N})^{s}_{mathrm{Sr}}}} and the spectral Neumann Laplacian <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msubsup> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mrow> <m:mo>-</m:mo> <m:msubsup> <m:mi mathvariant=normal>Δ</m:mi> <m:mi mathvariant=normal>Ω</m:mi> <m:mi>N</m:mi> </m:msubsup> </m:mrow> <m:mo stretchy=false>)</m:mo> </m:mrow> <m:mi>Sp</m:mi> <m:mi>s</m:mi> </m:msubsup> </m:math> {{(-Delta_{Omega}^{N})^{s}_{mathrm{Sp}}}} . In particular, we are interested in the attainability of Sobolev constants for these operators when Ω is a half-space." @default.
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- W2896482971 date "2018-10-11" @default.
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- W2896482971 title "Sobolev inequalities for fractional Neumann Laplacians on half spaces" @default.
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- W2896482971 doi "https://doi.org/10.1515/acv-2018-0020" @default.
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