Hölder Continuity of the Data to Solution Map for HR in the Weak Topology

Details Hölder Continuity of the Data to Solution Map for HR in the Weak Topology Hölder Continuity of the Data to Solution Map for HR in the Weak Topology

2011-11-25

arxiv.org/abs/1111.5879v1

Mathematics

Analysis of PDEs

12 pages, no figures

Scientific paper

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.

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