具有非线性斜导数边界条件的二阶完全非线性椭圆方程的障碍问题

THE OBSTACLE PROBLEMS FOR SECOND ORDER FULLY NONLINEAR ELLIPTIC EQUATIONS WITH NONLINEAR OBLIQUE DERIVATIVE BOUNDARY CONDITIONS

在自然结构条件下证明了具有非线性斜导数边界条件的二阶完全非线性随圆方程障碍问题Ｗ＾２，∞解的存在性，唯一性和正则性。抗议了Ｓ。Ｌｅｎｈａｒ，Ｐ。Ｌ。Ｌｉｏｎｓ和陈亚浙等人关于Ｄｉｒｉｃｈｌｅｔ边界条件的工作。

The paper proves the existence, uniqueness and regularity of the W￣(2.∞)solutions to the obstacle problems for second order fully nonlinear elliptic equations with the nonlinear oblique derivative boundary conditions, under the natural structure conditions. It extend the previous work of S. Lenhart, P.L. Lions and Chen Yazhe on Dirichlet boundary conditions.