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A Runge theorem for generalized analytic functions

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Author(s):
Campana, Camilo ; Hounie, Jorge Guillermo
Total Authors: 2
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