On a conjecture of J. Serrin

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Abstract

In 1964 J. Serrin proposed the following conjecture. Let u ε W loc1, 1 (ω) be a weak solution of the second order elliptic equation (1) below, in divergence form, with Holder continuous coefficients aij(x); then u is a "classical" solution. We announce a solution of this conjecture assuming onlyue BVloc(ω) and Dini continuous coefficients.

Original languageEnglish (US)
Pages (from-to)335-338
Number of pages4
JournalAtti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni
Volume19
Issue number4
DOIs
StatePublished - Jan 1 2008

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Divergence elliptic equations
  • Very weak solutions

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