Regularity of Weak Solutions

  • Jürgen Jost
Part of the Universitext book series (UTX)

Abstract

It is shown that under appropriate ellipticity assumptions, weak solutions of partial differential equations (PDEs) are smooth. This applies in particular to the Laplace equation for harmonic functions, thereby justifying Dirichlet’s principle introduced in the previous paragraph.

Keywords

Prool 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Jürgen Jost
    • 1
  1. 1.Max Planck Institute for Mathematics in the SciencesLeipzigGermany

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