DOCUMENTA MATHEMATICA, Vol. 9 (2004), 207-250

Xiaochun Liu and Ingo Witt

Asymptotic Expansions for Bounded Solutions to Semilinear Fuchsian Equations

It is shown that bounded solutions to semilinear elliptic Fuchsian equations obey complete asymptotic expansions in terms of powers and logarithms in the distance to the boundary. For that purpose, Schulze's notion of asymptotic type for conormal asymptotic expansions near a conical point is refined. This in turn allows to perform explicit computations on asymptotic types --- modulo the resolution of the spectral problem for determining the singular exponents in the asymptotic expansions.

2000 Mathematics Subject Classification: Primary: 35J70; Secondary: 35B40, 35J60

Keywords and Phrases: Calculus of conormal symbols, conormal asymptotic expansions, discrete asymptotic types, weighted Sobolev spaces with discrete asymptotics, semilinear Fuchsian equations

Full text: dvi.gz 89 k, dvi 239 k, ps.gz 1017 k, pdf 490 k.