Divergence forms of the ∞-Laplacian

Luigi D'Onofrio, Flavia Giannetti, Tadeusz Iwaniec, Juan Manfredi, Teresa Radice

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

The central theme running through our investigation is the ∞-Laplacian operator in the plane. Upon multiplication by a suitable function we express it in divergence form, this allows us to speak of weak ∞-harmonic function in W1,2. To every ∞-harmonic function u we associate its conjugate function v. We focus our attention to the first order Beltrami type equation for h = u + iv.

Original languageEnglish (US)
Pages (from-to)229-248
Number of pages20
JournalPublicacions Matematiques
Volume50
Issue number1
DOIs
StatePublished - Jan 1 2006

Keywords

  • ∞-Laplacian operator
  • ∞-harmonic functions

ASJC Scopus subject areas

  • Mathematics(all)

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  • Cite this

    D'Onofrio, L., Giannetti, F., Iwaniec, T., Manfredi, J., & Radice, T. (2006). Divergence forms of the ∞-Laplacian. Publicacions Matematiques, 50(1), 229-248. https://doi.org/10.5565/PUBLMAT_50106_13