Computer-assisted proofs for fixed point problems in Sobolev spaces

Alain Schenkel, Jan Wehr, Peter Wittwer

Research output: Contribution to journalArticle

6 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)1-67
Number of pages67
JournalMathematical Physics Electronic Journal
Volume6
StatePublished - 2000

Fingerprint

Sobolev space
Computer-assisted Proof
Fixed Point Problem
Sobolev Spaces
Convolution Product
Hierarchical Systems
analytic functions
Space of Analytic Functions
Critical Phenomena
Fast Fourier transform
convolution integrals
resistors
Error Estimates
Phase Transition
estimates
products

Keywords

  • Computer-assisted proofs
  • Constructive analysis in Sobolev spaces
  • Discrete convolutions are convolutions of splines
  • Phase transitions in random media

ASJC Scopus subject areas

  • Mathematical Physics

Cite this

Computer-assisted proofs for fixed point problems in Sobolev spaces. / Schenkel, Alain; Wehr, Jan; Wittwer, Peter.

In: Mathematical Physics Electronic Journal, Vol. 6, 2000, p. 1-67.

Research output: Contribution to journalArticle

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