Article
MSC:
35B30,
35B65,
35K90,
35K93,
46T20 | MR 2990180 | Zbl 1265.35019 | DOI: 10.1007/s10587-012-0033-6
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Keywords:
curve shortening flow; maximal regularity; local inverse function theorem
curve shortening flow; maximal regularity; local inverse function theorem
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.
References:
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