Let G be a classical group and let g be its Lie algebra. For a nilpotent element X E g, the ring R(Ox) of regular functions on the nilpotent orbit Ox is a G-module. In this thesis, we will decompose it into irreducible ...

In this thesis we use the method of moving planes to establish symmetry properties for positive solutions of semilinear elliptic equations. We give a detailed proof of the result due to Caffarelli, Gidas, and Spruck that ...