Timeline for Intuition for Agmon-Douglis-Nirenberg ellipticity
Current License: CC BY-SA 4.0
6 events
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| Feb 1 at 5:03 | comment | added | Igor Khavkine | @DeaneYang The paper of Volevich cited by Michael Renardy, which I've now summarized, actually addresses your point. Once you abstractly know that some choice of correct weights exists, ADN ellipticity can be checked without knowing them explicitly (by computing the scalar principal symbol of the "determinant" of the differential operator $D$). | |
| Feb 1 at 4:59 | history | edited | Igor Khavkine | CC BY-SA 4.0 |
Added discussion of how weights can be constructed.
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| Jan 26 at 9:12 | vote | accept | G. Blaickner | ||
| Jan 25 at 22:52 | history | edited | Igor Khavkine | CC BY-SA 4.0 |
added 1 character in body
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| Jan 25 at 19:35 | comment | added | Deane Yang | I would add that I think it is not possible to change the type of the PDE by changing the weights, except perhaps from degenerate to nondegenerate. So once the "correct" weights are found, one would be able to check whether it is elliptic or hyperbolic or someting else such as of real principal type. For example, I believe that the system of PDEs for an isometric embedding of a Riemannian manifold can be written as an ADN system whose type depends on the second fundamental form. | |
| Jan 25 at 19:02 | history | answered | Igor Khavkine | CC BY-SA 4.0 |