Remarks on viscosity solutions for fully nonlinear uniformly elliptic PDEs with measurable ingredients
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چکیده
We study the comparison principle and interior Holder continuity of viscosity solutions of F (x; u;Du;D 2 u) +H(x;Du) = f; where F satis es the standard \structure condition" and H has a superlinear growth with respect to Du. Following Ca arelli, Crandall, Kocan and Swi ech [3], we rst present the comparison principle between L p -viscosity subsolutions and L p -strong supersolutions. We next show the interior Holder continuity for C-viscosity solutions of the above equation. For this purpose, modifying some arguments in [1] by Ca arelli, we obtain the Harnack inequality for them when the growth order of H with respect to Du is less than 2.
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تاریخ انتشار 2007