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We consider solutions (and subsolutions and supersolutions) of the boundary value problem au(x,u,Du)DiJu + u(x,u,Du) = 0 in £2, s'(x)Diu + y(x)u = g(x) on3fi for a Lipschitz domain s, a positive-definite matrix-valued function (u'j), and a vector field s which points uniformly into Q. Without making any continuity assumptions on the known functions, we prove Harnack and Holder estimates for u near 3I2. In addition we bound the L°° norm of u near 3I2 in terms of an appropriate Lp norm and the known functions. Our approach is based on that for the corresponding interior estimates of Trudinger. This paper is concerned with analogs for solutions of oblique boundary value problems of the results in (10). Our results will extend previous work of Lieberman and Trudinger (5) and of Nadirashvili (9). Specifically we consider second order differential operators Q of the form

Local estimates for subsolutions and supersolutions of oblique derivative problems for general second order elliptic equations