TY - JOUR
T1 - Partial Di¤erential Equations
AU - D’Onofrio, Luigi
AU - Greco, Luigi
AU - Iwaniec, Tadeusz
AU - Schiattarella, Roberta
N1 - Funding Information:
The authors thank Professor Carlo Sbordone for support, encouragement and stimulating comments. Part of this research was carried out while L. D’Onofrio was visiting Mathematics Department of Syracuse University, and he wishes to thank SU for the hospitality and the oppurtunity. L. Greco was partially supported by ‘‘Progetto di Ateneo Federico II VATEX-MAT’’. T. Iwaniec was supported by the NSF grant DMS-1802107.
PY - 2018
Y1 - 2018
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
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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 -