Timeline for Embeddings of Bochner-Sobolev spaces with second time derivative
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Jul 16 at 10:03 | comment | added | Hannes | Well a priori only between $Y$ and $Z$ in your notation. There is a very comprehensive literature on Aubin-Lions type results so I recommend to start digging there for possible setups. For example in the seminal paper on Compact sets in the space $L^p(B)$ by Simon. | |
| Jul 15 at 10:11 | comment | added | MathsGoose | @Hannes Yes, you are right! Now I wonder whether $W$ should be between $X$ and $Y$ or $Y$ and $Z$ and what kind of embeddings does it have with its surrounding spaces? Because if the embeddings are compact, some special cases such as $W=Y$ will not be true. | |
| Jul 15 at 9:48 | comment | added | Hannes | That depends on the constellation with the Banach spaces, but you can of course apply the classical Aubin-Lions type results to the time derivative in the second order space setting to go for a continuously differentiable function space in time. | |
| Jul 15 at 8:38 | comment | added | MathsGoose | @Hannes What I had in mind is probably a better regularity in time for the space we embed in. For example, the first order space embed compactly in $C([0,T], W)$ where $W$ is a space between $X$ and $Y$ with given assumptions. For the second order space and since we have control over the second time derivative, would an embedding in $C^1([0,T], W)$ be valid? | |
| Jul 15 at 7:08 | comment | added | Hannes | It is a bit unclear to me what kind of result you expect or whether you want to pose different assumptions on the relation of $X,Y$ and $Z$. (Obviously anything that applies to the first-order space also aplies to the second-order space.) | |
| Jul 14 at 18:14 | history | edited | Daniele Tampieri | CC BY-SA 4.0 |
Corrected link
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| S Jul 14 at 17:22 | review | First questions | |||
| Jul 14 at 18:14 | |||||
| S Jul 14 at 17:22 | history | asked | MathsGoose | CC BY-SA 4.0 |