Timeline for Must a Schauder basis for $W^{1,p}_0(\Omega)$ be oscillatory?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Aug 22, 2021 at 9:00 | comment | added | mlk | @BigbearZzz To be honest I also just assumed that such a system should be possible. At least it looks to me like a bunch of triangle functions or something similar should do it, as this is more or less what all the finite-element people use, but that is not my area of expertise. | |
| Aug 22, 2021 at 8:05 | comment | added | BigbearZzz | I have one last question, if you don't mind. Do you happen to know where I can find a reference regarding a wavelets-like system forming a Schauder basis for $W^{1,p}_0(\Omega)$? I can easily imagine it being true for $p=2$ but I want to read more about other value of $p$. | |
| Aug 22, 2021 at 8:03 | vote | accept | BigbearZzz | ||
| Aug 21, 2021 at 19:50 | comment | added | mlk | @BigbearZzz If I am not fully mistaken, any wavelet-type basis would have your property. If the volume of the supports converges to 0, then the integral you gave will do so as well. | |
| Aug 21, 2021 at 12:47 | comment | added | BigbearZzz | Thanks a lot! Even if the statement turns out to be false for a general Schauder basis, the wavelets basis example seems to suggest that at least it should be possible to construct a basis with the (modified) property I asked? If this is true, do you know how regular $\Omega$ should be for such a construction to be possible? | |
| Aug 21, 2021 at 10:47 | history | answered | mlk | CC BY-SA 4.0 |