Variational Principles and Partial Differential Equations

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


Dirichlet’s principle consists in constructing harmonic functions by minimizing the Dirichlet integral in an appropriate class of functions. This idea is generalized, and minimizers of variational integrals are weak solutions of the associated differential equations of Euler and Lagrange. Several examples are discussed.


Partial Differential Equation Weak Solution Variational Principle Weak Convergence Lower Semicontinuity 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

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

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