JournalsrlmVol. 29, No. 4pp. 579–587

Poisson equation beyond its natural domain of definition

  • Luigi D'Onofrio

    Università degli Studi di Napoli Parthenope, Italy
  • Luigi Greco

    Università degli Studi di Napoli Federico II, Italy
  • Tadeusz Iwaniec

    Syracuse University, USA
  • Roberta Schiattarella

    Università degli Studi di Napoli Federico II, Italy
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Abstract

This note is concerned with the Poisson equation in the unit disk of the complex plane. Our setting is in the Sobolev space W1,p(D)\mathcal W^{1,p} (\mathbb D) with exponent 1<p<1 < p < \infty. Such a setting with p2p \neq 2 is referred to as beyond the natural domain of definition. The novelty lies in the use of a singular integral called Beurling Transform.

Cite this article

Luigi D'Onofrio, Luigi Greco, Tadeusz Iwaniec, Roberta Schiattarella, Poisson equation beyond its natural domain of definition. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 29 (2018), no. 4, pp. 579–587

DOI 10.4171/RLM/821