Besov regularity for solutions of p-harmonic equations

Albert Clop, Raffaella Giova, Antonia Passarelli Di Napoli

Research output: Contribution to journalArticleResearch

18 Citations (Scopus)

Abstract

© 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
JournalAdvances in Nonlinear Analysis
Volume8
DOIs
Publication statusPublished - 1 Jan 2019

Keywords

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

Fingerprint

Dive into the research topics of 'Besov regularity for solutions of p-harmonic equations'. Together they form a unique fingerprint.

Cite this