Archiv der Mathematik

, Volume 70, Issue 6, pp 470–478

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

  • Bernd Kawohl
  • Nikolai Kutev

DOI: 10.1007/s000130050221

Cite this article as:
Kawohl, B. & Kutev, N. Arch. Math. (1998) 70: 470. doi:10.1007/s000130050221

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.

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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