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It is shown that the data to solution map for the hyperelastic rod equationis 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 periodicand non-periodic cases. The proof is based on energy estimates coupled with adelicate commutator estimate and multiplier estimate.

H\"older Continuity of the Data to Solution Map for HR in the Weak Topology