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Functional Analysis and Its Applications

, Volume 38, Issue 3, pp 173–183 | Cite as

Remarks on the Uniqueness of a Solution of the Dirichlet Problem for Second-Order Elliptic Equations with Lower-Order Terms

  • V. V. Zhikov
Article

Abstract

We give an example of an incompressible diffusion equation whose solution is nonunique. It is shown that this equation has an approximation solution as well as another solution that cannot be obtained by approximation. We give sufficient conditions for the uniqueness of a solution as well as for the uniqueness of an approximation solution.

approximation solution nonuniqueness energy identity maximal function higher integrability 

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Copyright information

© Plenum Publishing Corporation 2004

Authors and Affiliations

  • V. V. Zhikov
    • 1
  1. 1.Vladimir State Pedagogical UniversityRussia

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