Timeline for Heat kernel for non bounded domains
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Feb 21, 2015 at 8:49 | vote | accept | Jop Kop | ||
| Feb 21, 2015 at 6:57 | comment | added | Andrew | In this question math.stackexchange.com/questions/266785/… it is proved for harmonic functions. The same argument holds for solutions of the heat equation. | |
| Feb 21, 2015 at 6:28 | comment | added | Jop Kop | Thank you for this wonderful argument! I suppose the pointwise limit still satisfies the heat equation, but I'm not sure why this is the case. Is this easy to see? | |
| Feb 20, 2015 at 15:15 | comment | added | Andrew | Yes, it doesn't directly work. One has to assume some conditions at infinity. Here is another argument. Denote $B_R=\{|x|<R\}$ a ball in $\mathbb R^n$. Suppose that there exists a monotone sequence $R_n\to\infty$ s.t. $U\cap B_{R_{n}}$ is regular enough and let $H_n$ be the corresponding solutions. Then $H_n\le K$ and for fixed values of parameters $(x,y,t)$ sequence $H_n$ is increasing. In such case there exists a pointwise limit of $H_n$, which will have all the required properties. | |
| Feb 19, 2015 at 18:15 | review | Low quality posts | |||
| Feb 19, 2015 at 18:28 | |||||
| Feb 19, 2015 at 18:08 | comment | added | Jop Kop | Hello Andrew. Which maximum principle do you refer to? Usually the maximum principle is proven only for bounded domains. In my case the domain is unfortunately unbounded. | |
| Feb 19, 2015 at 18:04 | history | edited | Andrew | CC BY-SA 3.0 |
added 4 characters in body
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| Feb 19, 2015 at 17:58 | history | answered | Andrew | CC BY-SA 3.0 |