Partial Di¤erential Equations

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

Research output: Contribution to journalArticle

Abstract

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
Volume29
Issue number4
DOIs
StatePublished - Jan 1 2018

Fingerprint

Singular Integrals
Poisson's equation
Argand diagram
Sobolev Spaces
Unit Disk
Exponent
Transform
Partial

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Partial Di¤erential Equations. / D’Onofrio, Luigi; Greco, Luigi; Iwaniec, Tadeusz; Schiattarella, Roberta.

In: Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni, Vol. 29, No. 4, 01.01.2018, p. 579-587.

Research output: Contribution to journalArticle

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