Regularity of Weak Solutions

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


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.


Weak Solution Schwarz Inequality Weak Equation Difference Quotient Sobolev Embedding Theorem 
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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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