Sobolev regularity of the second biharmonic problem on a rectangle

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Abstract

It is proved that for any f &esin; L 2(Ω) the weak solution of the second biharmonic problem on a rectangle satisfies u&esin; H 4(Ω). The proof uses the decomposition of the problem into two Poisson equations and a general condition for H 4-regularity via the eigenvalues and eigenfunctions of second order elliptic operators.

Original languageEnglish
Pages (from-to)255-259
Number of pages5
JournalActa Mathematica Hungarica
Volume109
Issue number3
DOIs
Publication statusPublished - Oct 1 2005

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Keywords

  • Biharmonic
  • Decomposition
  • Regularity

ASJC Scopus subject areas

  • Mathematics(all)

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