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Dec 3, 2021 at 20:28 comment added Student I did make progress on one problem where the weight was not radially symmetric. Turns out that if we write the linearized operator in polar coordinates, one can then perform separation of variables, which allows us to finish the proof.
Oct 22, 2021 at 22:03 history edited Student CC BY-SA 4.0
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Oct 22, 2021 at 22:02 comment added Student @GiuseppeNegro yeah you are right, I will fix that!
Oct 22, 2021 at 21:23 comment added Giuseppe Negro Shouldn't the first linearized equation be $-\Delta u = p U_{a, b}^{p-1}u$? The one you wrote does not seem linear to me.
Oct 22, 2021 at 20:58 history edited Student CC BY-SA 4.0
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Oct 20, 2021 at 12:05 comment added Student @GabS Yes, it is unique!
Oct 20, 2021 at 10:25 comment added GabS Is the positive solution unique for the divergence form operator?
Oct 20, 2021 at 8:24 history edited Student
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Oct 19, 2021 at 19:05 history asked Student CC BY-SA 4.0