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) |
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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 |
Keywords
- Beurling transform
- Laplace and Poisson equation
- PDEs in the complex plane
- Riemann–Hilbert problem
ASJC Scopus subject areas
- Mathematics(all)