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 | |
| State | Published - Jan 1 2018 |
Fingerprint
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 journal › Article
}
TY - JOUR
T1 - Partial Di¤erential Equations
AU - D’Onofrio, Luigi
AU - Greco, Luigi
AU - Iwaniec, Tadeusz
AU - Schiattarella, Roberta
PY - 2018/1/1
Y1 - 2018/1/1
N2 - 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.
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.
KW - Beurling transform
KW - Laplace and Poisson equation
KW - PDEs in the complex plane
KW - Riemann–Hilbert problem
UR - http://www.scopus.com/inward/record.url?scp=85061807323&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85061807323&partnerID=8YFLogxK
U2 - 10.4171/RLM/821
DO - 10.4171/RLM/821
M3 - Article
AN - SCOPUS:85061807323
VL - 29
SP - 579
EP - 587
JO - Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica E Applicazioni
JF - Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica E Applicazioni
SN - 1120-6330
IS - 4
ER -