Geodesic
Maximal regularity, the local inverse function theorem, and local well-posedness for the curve shortening flow
Czechoslovak Mathematical Journal, Tome 62 (2012) no. 2, pp. 335-346

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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.
DOI : 10.1007/s10587-012-0033-6
Classification : 35B30, 35B65, 35K90, 35K93, 46T20
Keywords: curve shortening flow; maximal regularity; local inverse function theorem 
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Boussandel, Sahbi; Chill, Ralph; Fašangová, Eva. Maximal regularity, the local inverse function theorem, and local well-posedness for the curve shortening flow. Czechoslovak Mathematical Journal, Tome 62 (2012) no. 2, pp. 335-346. doi: 10.1007/s10587-012-0033-6

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