On radial limit functions for entire solutions of second order elliptic equations in R2

• Autores: Peter V. Paramonov, André Boivin
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 42, Nº 2, 1998, págs. 509-519
• Idioma: inglés
• Títulos paralelos:
  • Funciones límites radiales para soluciones completas de ecuaciones elípticas de segundo orden en R2
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• Resumen

  • Given a homogeneous elliptic partial differential operator $L$ of order two with constant complex coefficients in $\bold R^2$, we consider entire solutions of the equation $Lu=0$ for which $$ \lim_{r \rightarrow \infty} u (re^{i\varphi}) =: U (e^{i\varphi}) $$ exists for all $\varphi \in [0, 2\pi)$ as a finite limit in $\bold C$. We characterize the possible "radial limit functions" $U$. This is an analog of the work of A. Roth for entire holomorphic functions. The results seem new even for harmonic functions.