Timeline for May the heat kernel of a connection Laplacian vanish?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Feb 21, 2019 at 16:25 | comment | added | RBega2 | An analytic function has the property that if it vanishes to infinity order at a point, then it vanishes identically in the appropriate component of its domain. This property is called the unique continuation property and turns out to hold for solutions of a general class of elliptic (and parabolic) equations (the point being that for solutions of an elliptic equation with analytic coefficients the solution is also analytic, but this property holds for rougher coefficients ). This paper projecteuclid.org/euclid.afm/1485898790 addresses the parabolic setting (so should apply to $h$). | |
| Feb 21, 2019 at 16:08 | comment | added | Alex M. | @RBega2: I do not come from the PDE "camp", therefore I do not follow you. Could you be a bit more explicit please? | |
| Feb 21, 2019 at 16:08 | comment | added | Alex M. | @ThomasRichard: Yes, both $L$ and its principal part are elliptic, but otherwise your comment is a bit enigmatic. Could you please clarify it a bit? | |
| Feb 21, 2019 at 16:05 | comment | added | Thomas Richard | for the case you are interested in, if I understand your notations, it seems to me that the leading term of L should be an elliptic operator, which might help. | |
| Feb 21, 2019 at 13:31 | comment | added | RBega2 | Have you tried looking at parabolic unique continuation results for your second question.? Those are quite robust (e.g. work for systems). | |
| Feb 21, 2019 at 9:40 | history | asked | Alex M. | CC BY-SA 4.0 |