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Archiv der Mathematik

, Volume 70, Issue 6, pp 470–478 | Cite as

Strong maximum principle for semicontinuous viscosity solutions of nonlinear partial differential equations

  • Bernd Kawohl
  • Nikolai Kutev

Abstract.

We derive a strong maximum principle for upper semicontinuous viscosity subsolutions of fully nonlinear elliptic differential equations whose dependence on the spatial variables may be discontinuous. Our results improve previous related ones for linear [18] and nonlinear [22] equations because we weaken structural assumptions on the nonlinearities. Counterexamples show that our results are optimal. Moreover they are complemented by comparison and uniqueness results, in which a viscosity subsolution is compared with a piecewise classical supersolution. It is curious to note that existence of a piecewise classical solution to a fully nonlinear problem implies its uniqueness in the larger class of continuous viscosity solutions.

Keywords

Differential Equation Partial Differential Equation Spatial Variable Maximum Principle Large Class 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag, Basel 1998

Authors and Affiliations

  • Bernd Kawohl
    • 1
  • Nikolai Kutev
    • 1
  1. 1.Mathematisches Institut, Universität Köln, D-50923 Köln, GermanyDE

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