Remarks on regularity of viscosity solutions for fully nonlinear uniformly elliptic PDEs with measurable ingredients

Shigeaki Koike, Toshimi Takahashi

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14 Citations (Scopus)


We study the comparison principle and interior Hölder continuity of viscosity solutions of F(x, u(x),Du(x),D2u(x)) + H(x,Du(x))-f(x) = 0 in O, where F satisfies the standard "structure condition" and H has superlinear growth with respect to Du. Following Caffarelli, Crandall, Kocan and Świȩch [3], we first present the comparison principle between Lp-viscosity subsolution and Lp-strong supersolutions. We next show the interior Hölder continuity for Lp-viscosity solutions of the above equation. For this purpose, modifying some arguments in [1] by Caffarelli, we obtain the Harnack inequality for them when the growth order of H with respect to Du is less than 2.

Original languageEnglish
Pages (from-to)493-512
Number of pages20
JournalAdvances in Differential Equations
Issue number4
Publication statusPublished - 2002 Dec 1


ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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