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manuscripta mathematica

, Volume 95, Issue 1, pp 59–77 | Cite as

Besov regularity for second order elliptic boundary value problems with variable coefficients

  • Stephan Dahlke
Article

Abstract

This paper is concerned with some theoretical foundations for adaptive numerical methods for elliptic boundary value problems. The approximation order that can be achieved by such an adaptive method is determined by certain Besov regularity of the weak solution. We study Besov regularity for second order elliptic problems in bounded domains in ℝ d . The investigations are based on intermediate Schauder estimates and on some potential theoretic framework. Moreover, we use characterizations of Besov spaces by wavelet expansions.

Key Words

elliptic boundary value problems adaptive methods nonlinear approximation Besov spaces wavelets Schauder estimates potential theory 

AMS Subject Classifications

primary 35B65 secondary 31B10 41A46 46E35 65N30 

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Copyright information

© Springer-Verlag 1998

Authors and Affiliations

  • Stephan Dahlke
    • 1
  1. 1.Institut für Geometrie und Praktische Mathematik RWTH AachenAachenGermany

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