Abstract
In this paper, we firstly use a variant of the moving plane method of Alexandroff to obtain radial symmetry of solutions for k-Hessian equations in annulus-type domains, which can be regarded as a generalization of Gidas–Ni–Nirenberg result in 1979. Then we consider an over-determined problem for k-Hessian equations in ring-shaped domains and prove the radial symmetry of the solutions and the domains.
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