Symmetry properties of semilinear elliptic equations with isolated singularities

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2007.Includes bibliographical references (p. 79-80).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 a solution in the punctured ball, B\{0}, behaves asymptotically like its spherical average at the origin. We also show that a solution with an isolated singularity in the upper half space Rn+ must be cylindrically symmetric about some axis orthogonal to the boundary aRn+.by Gregory Drugan.S.M