Besov regularity for solutions of p-harmonic equations

Albert Clop, Raffaella Giova, Antonia Passarelli Di Napoli

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33 Citations (Scopus)


© 2019 Walter de Gruyter GmbH, Berlin/Boston 2019. We establish the higher fractional differentiability of the solutions to nonlinear elliptic equations in divergence form, i.e., divA(x, Du) = div F, when A is a p-harmonic type operator, and under the assumption that x → A(x, ζ) belongs to the critical Besov-Lipschitz space B an/a,q∗ We prove that some fractional differentiability assumptions on F transfer to Du with no losses in the natural exponent of integrability. When div F = 0, we show that an analogous extra differentiability property for Du holds true under a Triebel- Lizorkin assumption on the partial map x → A(x, ζ).
Original languageEnglish
Pages (from-to)762-778
Number of pages17
JournalAdvances in Nonlinear Analysis
Issue number1
Publication statusPublished - 1 Jan 2019


  • Besov spaces
  • Nonlinear elliptic equations
  • Triebel-Lizorkin spaces
  • higher order fractional differentiability
  • p-harmonic operators


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