Regularity of solutions to the polyharmonic equation in general domains

Svitlana Mayboroda; Vladimir Maz'ya

Regularity of solutions to the polyharmonic equation in general domains

Analysis of PDEs 2012-06-04 v1

Authors: Svitlana Mayboroda , Vladimir Maz'ya

Abstract

The present paper establishes boundedness of $[m-\frac n2+\frac 12]$ derivatives for the solutions to the polyharmonic equation of order $2m$ in arbitrary bounded open sets of $\RR^n$ , $2\leq n\leq 2m+1$ , without any restrictions on the geometry of the underlying domain. It is shown that this result is sharp and cannot be improved in general domains. Moreover, it is accompanied by sharp estimates on the polyharmonic Green function.

Keywords

polyharmonic equation regularity boundedness of derivatives general domains Green function

Cite

@article{arxiv.1206.0081,
  title  = {Regularity of solutions to the polyharmonic equation in general domains},
  author = {Svitlana Mayboroda and Vladimir Maz'ya},
  journal= {arXiv preprint arXiv:1206.0081},
  year   = {2012}
}

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