A Note on the Sobolev and Gagliardo--Nirenberg Inequality when 𝑝 > 𝑁
It is known that the Sobolev space W1,p(ℝN){W^{1,p}(\mathbb{R}^{N})} is embedded into LNp/(N-p)(ℝN){L^{Np/(N-p)}(\mathbb{R}^{N})} if p<N{p<N} and into L∞(ℝN){L^{\infty}(\mathbb{R}^{N})} if p>N{p>N}. There is usually a discontinuity in the proof of those two different embeddings since...
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| Format: | Article |
| Language: | English |
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De Gruyter
2020-05-01
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| Series: | Advanced Nonlinear Studies |
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| Online Access: | https://doi.org/10.1515/ans-2020-2086 |