Timeline for System of divergence free vector fields
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| when toggle format | what | by | license | comment | |
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| 16 hours ago | comment | added | Paruru | Can you elaborate a bit more? I understood that $(\Delta f_1, \Delta f_2)^\prime = \tilde A ((\nabla f_1)^\prime, (\nabla f_2)^\prime)^\prime$ holds for some $\tilde A.$ Does this fit in the standard framework of elliptic PDE? | |
| 17 hours ago | history | edited | LSpice | CC BY-SA 4.0 |
Typo
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| 17 hours ago | history | edited | Paruru | CC BY-SA 4.0 |
added 45 characters in body
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| 18 hours ago | comment | added | mlk | It is a bit confusing, because in a usual elliptic operator the matrix would apply to the derivatives, not the components of $f$. But this means by product rule your PDE is equivalent to $A \Delta f = \text{ lower order terms}.$ So if $A$ is invertible everywhere we can multiply with $A^{-1}$ and get $\Delta f = \text{slightly different lower order terms}$ at which point uniqueness should follow from standard arguments for elliptic PDE. | |
| 22 hours ago | history | asked | Paruru | CC BY-SA 4.0 |