Given a homogeneous elliptic partial differential operator L of order two with constant complex coefficients in R2, we consider entire solutions of the equation Lu = 0 for which
limr→∞ u(reiφ) =: U(eiφ)
exists for all φ ∈ [0; 2π) as a finite limit in 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 seems new even for harmonic functions.
@article{urn:eudml:doc:41341,
title = {On radial limit functions for entire solutions of second order elliptic equations in R2.},
journal = {Publicacions Matem\`atiques},
volume = {42},
year = {1998},
pages = {509-519},
mrnumber = {MR1676041},
zbl = {0921.35023},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41341}
}
Boivin, André; Paramonov, Peter V. On radial limit functions for entire solutions of second order elliptic equations in R2.. Publicacions Matemàtiques, Tome 42 (1998) pp. 509-519. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41341/