Regularity of solutions to the polyharmonic equation in general domains

Svitlana Mayboroda, Vladimir Maz'ya

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

The present paper establishes boundedness of [m - n/2 + 1/2] derivatives for the solutions to the polyharmonic equation of order 2m in arbitrary bounded open sets of ℝn, 2 ≤ n ≤ 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.

Original languageEnglish (US)
Pages (from-to)1-68
Number of pages68
JournalInventiones Mathematicae
Volume196
Issue number1
DOIs
StatePublished - 2014

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