Local estimates for subsolutions and supersolutions of oblique derivative problems for general second order elliptic equations
Local estimates for subsolutions and supersolutions of oblique derivative problems for general second order elliptic equations
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DOI：
10.1090/s0002-9947-1987-0906819-0
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发表时间：
1987
影响因子：
1.3
通讯作者：
G. M. Lieberman
中科院分区：
文献类型：
--
作者：
G. M. Lieberman
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
