Timeline for Poisson equations for tensors on compact Riemannian manifold
Current License: CC BY-SA 4.0
6 events
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| Mar 6, 2023 at 11:20 | comment | added | B.Hueber | Thank you very much! | |
| Mar 6, 2023 at 11:11 | comment | added | Liviu Nicolaescu | The Laplacian over tensors is also a symmetric operator. Denote by $H_k\subset C^\infty (T^*M^{\otimes k})$ the space of harmonic tensors. Fredholm alternative states that the equation $\Delta T=S$ has a solution iff $S$ is $L^2$-orthogonal to $H_k$. For details see Sec. 10.4.1 of www3.nd.edu/~lnicolae/Lectures.pdf | |
| Mar 6, 2023 at 11:08 | history | edited | Liviu Nicolaescu | CC BY-SA 4.0 |
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| Mar 6, 2023 at 11:08 | comment | added | Romain Gicquaud | You can safely use the Fredholm alternative. The existence and uniqueness of the solution (up to regularity issues) is guaranteed by the Lax-Milgram theorem. | |
| Mar 6, 2023 at 11:07 | history | edited | Liviu Nicolaescu | CC BY-SA 4.0 |
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| Mar 6, 2023 at 10:14 | history | asked | B.Hueber | CC BY-SA 4.0 |