A Runge theorem for generalized analytic functions期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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A Runge theorem for generalized analytic functions

Authors:	Camilo Campana Jorge Guillermo Hounie

Institution:	1. Departamento de Matemática, Universidade Federal de Santa Catarina, Florianópolis, Santa Catarina, Brazil;2. Departamento de Matemática, Universidade Federal de São Carlos, São Carlos, São Paulo, Brazil

Abstract:	We show an approximation theorem of Runge type for solutions of the generalized Vekua equation $L u = A u + B \bar{u} $Lu = Au + B \overline{u}$$ , where L belongs to a class of degenerate elliptic planar vector fields and $A, B \in L^{p} $A,B \in L^{p}$$ . 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 $L u = A u + B \bar{u} + f $Lu = Au + B \overline{u} + f$$ with $f \in L^{p} $f \in L^{p}$$ and some of its consequences.

Keywords:	degenerate elliptic equations generalized analytic functions locally integral vector fields Runge's theorem