Boundedness of the hessian of a biharmonic function in a convex domain

Svitlana Mayboroda, Vladimir Maz'ya

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

We consider the Dirichlet problem for the biharmonic equation on an arbitrary convex domain and prove that the second derivatives of the variational solution are bounded in all dimensions.

Original languageEnglish (US)
Pages (from-to)1439-1454
Number of pages16
JournalCommunications in Partial Differential Equations
Volume33
Issue number8
DOIs
StatePublished - Aug 26 2008

Keywords

  • Biharmonic equation
  • Convex domain
  • Dirichlet problem

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