David Karapetyan
Published 2011-11-25Version 1
It is shown that the data to solution map for the hyperelastic rod equation is H\"older continuous from bounded sets of Sobolev spaces with exponent $s > 3/2$ measured in a weaker Sobolev norm with index $r < s$ in both the periodic and non-periodic cases. The proof is based on energy estimates coupled with a delicate commutator estimate and multiplier estimate.
Comments: 12 pages, no figures
On the well-posedness of the hyperelastic rod equation
Almost everywhere Hölder continuity of gradients to non-diagonal parabolic systems
Hölder continuity and injectivity of optimal maps
![QR code for arXiv:1111.5879 [math.AP]](http://oss.arxitics.com/images/favicon.svg)