Timeline for A result on the convergence of the vanishing viscosity approximation to the viscosity solution of an IVP for Hamilton-Jacobi equation
Current License: CC BY-SA 3.0
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| Oct 28, 2016 at 22:54 | comment | added | parsiad | In terms of first-order equations, you can use the "passage to limits" result above and simply remove the $D^2$ terms. In terms of making the results sharper, you should be able to relax the above so that each $F_\epsilon$ is only USC instead of continuous (and LSC for the subsolution case). As for other results on approximation schemes, I recommend looking at the first paragraph of the Barles-Souganidis paper, in which the authors list approximation results for special cases (including Hamilton-Jacobi, if my memory serves me correctly). | |
| Oct 28, 2016 at 22:48 | history | edited | parsiad | CC BY-SA 3.0 |
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| Oct 28, 2016 at 21:18 | comment | added | user99249 | Yes, thanks (and thank you very much for following up): the works you have pointed out look very interesting; I hope to get around to read them more carefully shortly. Do you also know some expositions of the result (or slightly sharper results) obtained by Crandall and Lions for first-order equations? | |
| Oct 26, 2016 at 23:05 | comment | added | parsiad | @Kei: was my answer useful? I'm interested to see if this is what you were looking for. (just following up here) | |
| Oct 19, 2016 at 20:11 | history | edited | parsiad | CC BY-SA 3.0 |
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| Oct 19, 2016 at 19:43 | history | edited | parsiad | CC BY-SA 3.0 |
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| Oct 19, 2016 at 19:38 | history | answered | parsiad | CC BY-SA 3.0 |