A Runge theorem for generalized analytic functions

We show an approximation theorem of Runge type for solutions of the generalized Vekua equation Lu=Au+Bu¯$Lu = Au + B \overline{u}$, where L belongs to a class of degenerate elliptic planar vector fields and A,B∈Lp$A,B \in L^{p}$. To prove the theorem, we make use of an integral representation for th...

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Bibliographic Details
Published in:Mathematische Nachrichten 2023-09, Vol.296 (9), p.3856-3876
Main Authors: Campana, Camilo, Hounie, Jorge Guillermo
Format: Article
Language:English
Subjects:
Analytic functions
degenerate elliptic equations
Fields (mathematics)
generalized analytic functions
locally integral vector fields
Mathematical analysis
Runge's theorem
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Summary:We show an approximation theorem of Runge type for solutions of the generalized Vekua equation Lu=Au+Bu¯$Lu = Au + B \overline{u}$, where L belongs to a class of degenerate elliptic planar vector fields and A,B∈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¯+f$Lu = Au + B \overline{u} + f$ with f∈Lp$f \in L^{p}$ and some of its consequences.
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.202100011