Timeline for Viscosity solution of the PDE
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 13, 2015 at 19:28 | comment | added | Jeff | You can use Perron's method for existence (which is covered in the User's Guide). You can also check the book by Bardi and Dolcetta "Optimal control and viscosity solutions of HJB equations", as they study HJ-equations of this form. | |
| Jan 16, 2013 at 21:37 | comment | added | nick | Indeed, the proof on MSE is wrong. Theorem 1,/10.2 is about uniqueness, but how about existence? I am trying now to adapt that proof for uniqueness result. | |
| Jan 16, 2013 at 0:45 | comment | added | Luis Silvestre | Yes, but the proof in math.stackexchange is wrong because the functions $\phi$ may not exist if $u_1$ and $u_2$ are not differentiable at $x_0$. The classical proof uses the doubling of variables method, very much like in the proof of Theorem 1 in section 10.2 of Evans book. | |
| Jan 15, 2013 at 23:41 | comment | added | nick | The answer already appeared here: math.stackexchange.com/questions/278384/viscosity-solutions/… | |
| Jan 15, 2013 at 17:27 | comment | added | Luis Silvestre | This is literally the first example I saw when I studied viscosity solutions in grad school. Have you checked the users guide to viscosity solutions for a general existence and unique theorem? | |
| Jan 14, 2013 at 14:57 | comment | added | nick | This stands for gradient of $u.$ | |
| Jan 14, 2013 at 14:49 | comment | added | Andrey Rekalo | What is $|Du|$? | |
| Jan 14, 2013 at 14:43 | history | asked | nick | CC BY-SA 3.0 |