Symmetry properties of semilinear elliptic equations with isolated singularities

• Main Author: Drugan, Gregory (Gregory Michael)
• Other Authors: David Jerison.
• Format: Others
• Language: English
• Published: Massachusetts Institute of Technology 2007
• Subjects: Mathematics.
• Online Access: http://hdl.handle.net/1721.1/38999

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.