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

David Karapetyan

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

Analysis of PDEs 2011-11-28 v1

Authors: David Karapetyan

Abstract

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.

Keywords

hyperelastic rod equation Hölder continuity data to solution map weak topology Sobolev spaces commutator estimate multiplier estimate

Cite

@article{arxiv.1111.5879,
  title  = {H\"older Continuity of the Data to Solution Map for HR in the Weak Topology},
  author = {David Karapetyan},
  journal= {arXiv preprint arXiv:1111.5879},
  year   = {2011}
}

Comments

12 pages, no figures

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