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 , 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  by Caffarelli, we obtain the Harnack inequality for them when the growth order of H with respect to Du is less than 2.
|ジャーナル||Advances in Differential Equations|
|出版ステータス||Published - 2002 12 1|
ASJC Scopus subject areas
- Applied Mathematics