PDE and Applied Mathematics Seminar[ Edit ]
Moderator: Gershon Wolansky
In this talk we will derive sufficient conditions for the absence of embedded eigenvalues of two-dimensional magnetic Schroedinger operators. The limiting absorption principle will be discussed as well. This is a joint work with S.Avramska-Lukarska and D.Hundertmark.
Affine Sobolev inequality of G. Zhang is a refinement of the usual limiting Sobolev inequality which possesses additional invariance with respect to action of the group SL(N) of unimodular matrices. For p=2 we find a simplified form of the affine Sobolev functional and study the related affine Laplacian. For general p<N we study compactness properties of the functional and existence of minimizers. This is a joint work with Ian Schindler.