On differentiability of Sobolev functions with respect to the Sobolev norm
We study connections between the Wp1$W^1_p$‐differentiability and the Lp$L_p$‐differentiability of Sobolev functions. We prove that Wp1$W^1_p$‐differentiability implies the Lp$L_p$‐differentiability, but the opposite implication is not valid. The notion of approximate differentiability is discussed...
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Veröffentlicht in: | Mathematische Nachrichten 2024-10, Vol.297 (10), p.3681-3699 |
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Hauptverfasser: | , , |
Format: | Artikel |
Sprache: | eng |
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Online-Zugang: | Volltext |
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Zusammenfassung: | We study connections between the Wp1$W^1_p$‐differentiability and the Lp$L_p$‐differentiability of Sobolev functions. We prove that Wp1$W^1_p$‐differentiability implies the Lp$L_p$‐differentiability, but the opposite implication is not valid. The notion of approximate differentiability is discussed as well. In addition, we consider the Wp1$W^1_p$‐differentiability of Sobolev functions capp$\operatorname{cap}_p$‐almost everywhere. |
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ISSN: | 0025-584X 1522-2616 |
DOI: | 10.1002/mana.202300545 |