Partial Di¤erential Equations

Luigi D’Onofrio, Luigi Greco, Tadeusz Iwaniec, Roberta Schiattarella

Research output: Contribution to journalArticlepeer-review


This note is concerned with the Poisson equation in the unit disk of the complex plane. Our setting is in the Sobolev space W 1; p ðDÞ with exponent 1 < p < l. Such a setting with p A 2 is referred to as beyond the natural domain of definition. The novelty lies in the use of a singular integral called Beurling Transform.

Original languageEnglish (US)
Pages (from-to)579-587
Number of pages9
JournalAtti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni
Issue number4
StatePublished - 2018


  • Beurling transform
  • Laplace and Poisson equation
  • PDEs in the complex plane
  • Riemann–Hilbert problem

ASJC Scopus subject areas

  • General Mathematics


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