Timeline for Weird claims and conclusions in "Introduction to Shape Optimization"
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 28, 2020 at 15:04 | vote | accept | 0xbadf00d | ||
| Aug 14, 2020 at 1:59 | comment | added | David Roberts♦ | @DCM better to also give a human-readable reference, in case that url breaks: M. C. Delfour, Structure of Shape Derivatives for Nonsmooth Domains, J. Funct. Analysis 104 (1992) 1-33 and here's a stable doi link: doi.org/10.1016/0022-1236(92)90087-Y | |
| Aug 13, 2020 at 19:04 | answer | added | DCM | timeline score: 2 | |
| Aug 13, 2020 at 4:57 | comment | added | 0xbadf00d | @DCM The content of this is paper is also in the book. But it does not explain, for example, why $V(t,x)$ is differentiable with resepect $x$ as claimed in (2.76). | |
| Aug 12, 2020 at 19:23 | comment | added | DCM | It does things the other way round (i.e. start with the vector field and define the 1-parameter family via solutions to the associated ODE with different initial conditions). | |
| Aug 12, 2020 at 19:21 | comment | added | DCM | I think this is the original paper: core.ac.uk/download/pdf/82336011.pdf | |
| Aug 12, 2020 at 13:07 | comment | added | 0xbadf00d | @leomonsaingeon Thank you for your comment. Yeah, that's basically what I thought, but at other places they consider the velocities to belong to $C^k(\mathbb R^N,\mathbb R^N)$. Maybe they think on shape functionals given by integral functionals whose integrands are locally integrable and that's why they assume compact support. Oh, and they explicitly define the spaces $C_0^\infty(\Omega,\mathbb R^d)$ as the space of smooth functions which are compactly supported. Shouldn't they denote this space by $\mathcal D^\infty(\Omega,\mathbb R^d)$ or $\mathcal D(\Omega,\mathbb R^d)$? Confusing ... | |
| Aug 12, 2020 at 10:46 | comment | added | leo monsaingeon | I don't know about your main issues, but what I can tell you is that $\mathcal D$ usually stands for the space of smooth, compactly supported test-functions, while the (dual) space of distributions is usually denoted as $\mathcal D'$. So I guess in this context $\mathcal D^k(\mathbb R^N;\mathbb R^N)$ should stand for the space of compactly supported $C^k$ functions from $\mathbb R^N$ into $\mathbb R^N$. (This seems consistent with the use that the authors seem to make in your displayed excerpts of the paper) | |
| Aug 12, 2020 at 10:37 | history | asked | 0xbadf00d | CC BY-SA 4.0 |