Abstract
In this paper, we prove the symmetry and monotonicity results of viscosity solutions for fully nonlinear elliptic equations F(D2u,Du,u,x)=0 and fully nonlinear parabolic equations −ut+F(D2u,Du,u,x,t)=0 in annular domains by using the method of moving planes. We also prove the symmetry and monotonicity results of viscosity solutions for fully nonlinear parabolic equations −ut+F(D2u,Du,u,t)=0 in exterior domains. This extends the results of fully nonlinear elliptic equations in exterior domains.
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