Abstract
This paper is concerned with a class of boundary value problems for fully nonlinear elliptic PDEs involving the p-Hessian operator. We first derive a maximum principle for a suitable function involving the solution u(x) and its gradient. This maximum principle is then applied to obtain some sharp estimates for the solution and the magnitude of its gradient. We also investigate some symmetry properties of Ω or u(x) under specific boundary condition or geometry of Ω.
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