Partial Di¤erential Equations

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

doi:10.4171/RLM/821

Partial Di¤erential Equations

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

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	579-587
Number of pages	9
Journal	Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni
Volume	29
Issue number	4
DOIs	https://doi.org/10.4171/RLM/821
State	Published - 2018

Keywords

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

ASJC Scopus subject areas

General Mathematics

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10.4171/RLM/821

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AU - D’Onofrio, Luigi

AU - Greco, Luigi

AU - Iwaniec, Tadeusz

AU - Schiattarella, Roberta

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AB - 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.

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KW - Laplace and Poisson equation

KW - PDEs in the complex plane

KW - Riemann–Hilbert problem

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Partial Di¤erential Equations

Abstract

Keywords

ASJC Scopus subject areas

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