A generalized CR equation with isolated singularities

Abstract

The generalized CR equation $u_{\overline{z}}=au+b\overline{u}+f$ is studied when the coefficients a and b have a finite number of singular points inside the domain. Solutions are constructed via the study of an associated integral operator and the existence of nontrivial solutions of the associated homogeneous equation is established.

Keywords:

• CR equation
• integral operator
• singular points

AMS Subject Classifications:

• Primary: 30G20
• Secondary: 35F05

Acknowledgments

Part of this work was done when the first author was visiting the Department of Mathematics & Statistics at FIU (Florida International University). He would like to thank the members of the institution for the support provided during his visit.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The first author was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES[88882.381834/2019-01]) - Finance Code 001 and in part by São Paulo Research Foundation (FAPESP) [grant number 2021/03199-9]