Inverting the p-harmonic operator

Luigi Greco, Tadeusz Iwaniec, Carlo Sbordone

Research output: Contribution to journalArticlepeer-review

236 Scopus citations


The paper is concerned with the nonhomogeneous p-harmonic equation div |▽u|p-2▽u = div f . The main object is the operator H which carries given vector function f into the gradient field ▽u. The natural domain of H is the Lebesgue space Lq(Ω, ℝn), where 1/p + 1/q = 1. We extend the operator H to slightly larger spaces called grand Lq-spaces. Continuity of H is used to prove existence and uniqueness results for nonhomogeneous n-harmonic type equations div A(x, Vu) = μ with μ a Radon measure.

Original languageEnglish (US)
Pages (from-to)249-258
Number of pages10
JournalManuscripta Mathematica
Issue number2
StatePublished - Feb 1997

ASJC Scopus subject areas

  • General Mathematics


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