Timeline for Are solutions to this elliptic PDE uniformly bounded in $\mathbb{R}^n?$
Current License: CC BY-SA 4.0
9 events
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| Jul 10, 2021 at 9:05 | history | edited | Daniele Tampieri | CC BY-SA 4.0 |
Minor Math Jaxing (used $\|\cdot\|$ instead of $||\cdot||$)
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| Jul 8, 2021 at 14:47 | comment | added | Willie Wong | In dimension 3 for example, $u\in \dot{H}^1\implies u \in L^6$, and thus $\rho u \in L^6$ and inverting the Laplacian (you don't need De Giorgi-Nash-Moser here, can get away with boundedness of Riesz transform) gives you $u\in W^{2,6}$ which gives that $u\in C^{1,\alpha}$ (no "loc"). | |
| Jul 8, 2021 at 14:24 | comment | added | Student | By standard elliptic regularity theory, I had De Giorgi-Nash-Moser theorem which works for elliptic equations with bounded and measurable coefficients. | |
| Jul 8, 2021 at 14:22 | comment | added | Student | One can view $\lambda$ as an eigenvalue and $\phi$ as the corresponding eigenfunction. | |
| Jul 8, 2021 at 14:22 | comment | added | Student | @WillieWong I fixed the embedding, it happens in the weighted Lp space. | |
| Jul 8, 2021 at 14:19 | history | edited | Student | CC BY-SA 4.0 |
added 27 characters in body
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| Jul 8, 2021 at 10:01 | history | edited | Student | CC BY-SA 4.0 |
edited tags
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| Jul 8, 2021 at 9:46 | history | edited | Student |
edited tags
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| Jul 8, 2021 at 8:14 | history | asked | Student | CC BY-SA 4.0 |