Timeline for Integral representation of solution of an elliptic PDE in divergence form
Current License: CC BY-SA 4.0
5 events
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| May 26, 2021 at 21:16 | comment | added | Giorgio Metafune | If $Lu=0$, write $u(x)=u(x)+\int_{\Omega} G(x,y) Lu(y)dy$ and integrate by parts twice. Formally you get your formula since $G$ is symmetric and $L_y G(x,y)= \delta_x$. It should be possible to justify it by using the heat kernel, which is more regular for $t>0$ but I am not sure about the regularity on $A$ needed for this. | |
| May 26, 2021 at 20:18 | comment | added | username | Can you detail how you came to that formula? You integrated by parts against something, then took a limit, probably? | |
| May 26, 2021 at 16:59 | history | edited | Harish | CC BY-SA 4.0 |
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| May 26, 2021 at 16:14 | history | edited | Harish | CC BY-SA 4.0 |
added 105 characters in body
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| May 26, 2021 at 13:58 | history | asked | Harish | CC BY-SA 4.0 |