Alain Schenkel, Jan Wehr, Peter Wittwer
Computer-Assisted Proofs for Fixed Point Problems in
Sobolev Spaces
(2342K, plain TeX with embedded PS figs. and Section.8.tar.gz.uu)
ABSTRACT. In this paper we extend the technique of computer-assisted
proofs to fixed point problems in Sobolev spaces. Up to now
the method was limited to the case of spaces of analytic
functions. The possibility to work with Sobolev spaces is an
important progress and opens up many new domains of
applications. Our discussion is centered around a concrete
problem that arises in the theory of critical phenomena and
describes the phase transition in a hierarchical system of
random resistors. For this problem we have implemented in
particular the convolution product based on the Fast Fourier
Transform (FFT) algorithm with rigorous error estimates.