The Harnack Estimate Of Solution For A Class Of Hessian Equations In Geometric Optics

This article concerns about the Harnack estimates of solutions for a class of Hessian equations: which arises from geometric optics. The main method is to employ Bernstein's technique with a suitable test function, by which we can obtain the logarithmic gradient estimates of positive solutions and Hanack inequalities umax?Cumin.