| Title:
|
Maximal regularity, the local inverse function theorem, and local well-posedness for the curve shortening flow (English) |
| Author:
|
Boussandel, Sahbi |
| Author:
|
Chill, Ralph |
| Author:
|
Fašangová, Eva |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
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1572-9141 (online) |
| Volume:
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62 |
| Issue:
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2 |
| Year:
|
2012 |
| Pages:
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335-346 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Local well-posedness of the curve shortening flow, that is, local existence, uniqueness and smooth dependence of solutions on initial data, is proved by applying the Local Inverse Function Theorem and $L^2$-maximal regularity results for linear parabolic equations. The application of the Local Inverse Function Theorem leads to a particularly short proof which gives in addition the space-time regularity of the solutions. The method may be applied to general nonlinear evolution equations, but is presented in the special situation only. (English) |
| Keyword:
|
curve shortening flow |
| Keyword:
|
maximal regularity |
| Keyword:
|
local inverse function theorem |
| MSC:
|
35B30 |
| MSC:
|
35B65 |
| MSC:
|
35K90 |
| MSC:
|
35K93 |
| MSC:
|
46T20 |
| idZBL:
|
Zbl 1265.35019 |
| idMR:
|
MR2990180 |
| DOI:
|
10.1007/s10587-012-0033-6 |
| . |
| Date available:
|
2012-06-08T09:37:31Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142832 |
| . |
| Reference:
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