A Runge theorem for generalized analytic functions

Camilo Campana and Jorge Guillermo Hounie

Mathematische Nachrichten, 2023, vol. 296, issue 9, 3856-3876

Abstract: 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.

Date: 2023
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https://doi.org/10.1002/mana.202100011

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