Timeline for Alternative definitions of Sobolev spaces on non-compact Riemannian manifolds
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Aug 26, 2019 at 6:58 | comment | added | user590533 | Good observation: actually, in the aforementioned reference the result is only stated and not proved. But your remark is perfectly legitimate. | |
| Aug 23, 2019 at 22:52 | comment | added | Jesse Railo | Is it clear that always $W^{k,p}(M) \subset L_k^p(M)$? It seems that the result you stated characterize the closure of smooth compactly supported functions with respect to the Sobolev norms. Does the condition $||\nabla u ||_p < \infty$ imply that $Pu \in L^p(M)$ for any smooth differential operator $P$ of order $1$? For example, you may choose the coefficients of a smooth differential operator $P$ to be unbounded since the manifold itself is noncompact. | |
| Apr 1, 2019 at 8:10 | review | Late answers | |||
| Apr 1, 2019 at 8:24 | |||||
| Apr 1, 2019 at 7:55 | review | First posts | |||
| Apr 1, 2019 at 8:33 | |||||
| Apr 1, 2019 at 7:51 | history | answered | user590533 | CC BY-SA 4.0 |