Timeline for What was Weierstrass's counterexample to the Dirichlet Principle?
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
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| Sep 17, 2023 at 17:27 | comment | added | No-one | If someone is interested, the explicit function is $u(r,\theta)=\sum_{n=1}^\infty\frac{1}{n^2}r^{n!}\sin(n!\theta)$. | |
| Sep 15, 2013 at 5:08 | comment | added | timur | @Will: Yes, but Hadamard's example is of different nature. That said, similar example was discovered by Friedrich Prym around 1870's. | |
| Oct 15, 2010 at 4:46 | comment | added | Will Jagy | Willie, I found a biography of Courant by Peter D. Lax and a book called Hilbert-Courant by Constance Reid. Weierstrass objected first, while Riemann was still alive. Lax says "Weierstrass even gave an example of a fourth order functional whose minimum is not assumed by any function." Hadamard's example is later, 1906. | |
| Oct 14, 2010 at 22:07 | comment | added | Willie Wong | Ah, I may have confused Weierstrass and Hadamard on this matter. Thanks, Will! | |
| Oct 14, 2010 at 21:38 | comment | added | Will Jagy | Willie, I was just at a bookstore, Courant gives an example, due to Hadamard, where the original formulation of the Dirchlet principle fails (integral undefined or something), but there is a solution on the unit disc with $\Delta u = 0$ and with the given boundary data. | |
| Oct 14, 2010 at 17:47 | comment | added | Will Jagy | likely to be in Richard Courant, "Dirichlet's Principle, Conformal Mapping, and Minimal Surfaces" Dover Publications | |
| Oct 14, 2010 at 17:36 | history | answered | Willie Wong | CC BY-SA 2.5 |