Timeline for Is the integral functional $I(x) = \int_{0}^{T} \Lambda (t , x(t), \dot{x} (t)) \; dt $ locally lipschitz on the space $C^2 [0 ,T] $?
Current License: CC BY-SA 4.0
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| Jun 9, 2020 at 21:01 | vote | accept | Red shoes | ||
| Jun 8, 2020 at 17:59 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Jun 8, 2020 at 17:52 | comment | added | Iosif Pinelis | In fact, $I$ is not locally Lipschitz. | |
| Jun 8, 2020 at 17:51 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Jun 8, 2020 at 17:38 | comment | added | Red shoes | Btw, when I want to apply DCT, I'm not sure how to choose the dominating function below to switch the integral and limit ? $$\lim_{n \to \infty} \int_{0}^{T} \frac{\Lambda (t , x(t)+ \tau_n h(t), \dot{x} (t)+ \tau_n \dot{h}(t)) - \Lambda (t , x(t), \dot{ x} (t))}{\tau_n}$$ | |
| Jun 8, 2020 at 16:27 | comment | added | Red shoes | I'm actually trying to show that $I$ is Frechet differentiable ! That's why I asked this question. Do you have any reference in your mind regarding this issue ? Thanks in advance. | |
| Jun 8, 2020 at 12:57 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Jun 8, 2020 at 6:44 | comment | added | Red shoes | Why is $I$ differentiable at first place ? | |
| Jun 8, 2020 at 1:00 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |