A Runge theorem for generalized analytic functions

Author(s)

Campana, Camilo ; Hounie, Jorge Guillermo

• Document type: Journal article
• Source: Mathematische Nachrichten; v. 296, n. 9, p. 21-pg., 2023-06-22.

Abstract

We show an approximation theorem of Runge type for solutions of the generalized Vekua equation Lu=Au+Bu over bar $Lu = Au + B \overline{u}$, where L belongs to a class of degenerate elliptic planar vector fields and A,B & ISIN;Lp$A,B \in L<^>{p}$. To prove the theorem, we make use of an integral representation for the solutions of the generalized Vekua equation valid on relatively compact sets. As an application, we study the global solvability of the equation Lu=Au+Bu over bar +f$Lu = Au + B \overline{u} + f$ with f & ISIN;Lp$f \in L<^>{p}$ and some of its consequences. (AU)

• FAPESP's process: 18/14316-3 - Geometric theory of PDE and multidimensional complex analysis
• Grantee: Paulo Domingos Cordaro
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 16/21969-8 - The Riemann Hilbert Problem for degenerate elliptic vector fields
• Grantee: Camilo Campana
• Support Opportunities: Scholarships in Brazil - Post-Doctoral