Timeline for Estimates on gradients of diffusion semigroups
Current License: CC BY-SA 3.0
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| Feb 8, 2014 at 19:45 | comment | added | Nate Eldredge | So I think what you really want is an $L^r$ estimate on the gradient of the heat kernel. Then your desired estimate follows from differentiating under the integral sign and using Holder's inequality. There should be tons of work on estimating the gradient of the heat kernel; I don't have references off the top of my head but if you can't find any, I'll try to add something in the next couple days. | |
| Feb 8, 2014 at 17:48 | comment | added | guest | @Nate Eldredge I have edited the post. It was not clearly written, I wanted it to mean that the constant is dependent on $t$. The estimates that you mention are not of IMMEDIATE interest to me, but I would love to know about them as well. I will really appreciate some references on them. | |
| Feb 8, 2014 at 17:47 | history | edited | guest | CC BY-SA 3.0 |
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| Feb 8, 2014 at 16:40 | comment | added | Nate Eldredge | It seems unlikely, since clearly no such bound can hold as $t \to 0$ (consider a small but wiggly $f$). However, estimates like $\| \nabla e^{t \Delta} f \|_p \le \|\nabla f\|_q$ have been studied - would that be of interest to you? | |
| Feb 8, 2014 at 16:05 | history | edited | guest | CC BY-SA 3.0 |
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| Feb 8, 2014 at 1:49 | history | edited | guest | CC BY-SA 3.0 |
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| Feb 8, 2014 at 1:41 | history | edited | guest | CC BY-SA 3.0 |
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| Feb 7, 2014 at 19:11 | review | First posts | |||
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| Feb 7, 2014 at 18:56 | history | asked | guest | CC BY-SA 3.0 |