Mathematics Colloquium: Tornado solutions and continuity for semilinear elliptic PDEs in the plane
4:10 p.m. Neill Hall 5W
Abstract: We show continuity of bounded positive solutions to some semilinear elliptic equations Δu = f(u) in domains of R2. Our technique involves ruling out sequences of solutions that we call ``tornado solutions,' and does not assume the variational stability that is required in other treatments of these equations. We will also discuss the use of our results in constructing singular solutions, alternative techniques of other authors, and the relation to the general study of singularities of minimal hypersurfaces in Euclidean space.