5 research outputs found
The Stepanov differentiability theorem in metric measure spaces
We extend Cheeger's theorem on differentiability of Lipschitz functions in metric measure spaces to the class of functions satisfying Stepanov's condition. As a consequence, we obtain the analogue of Calderon's differentiability theorem of Sobolev functions in metric measure spaces satisfying a Poincaré inequalit
Local compactness and closedness for families of <math> <?Pub Eqn> <f> <sc>A</sc></f> </math>-harmonic functions.
We show that closed families of A -harmonic functions whose members all admit a common growth condition admits many topologies, all of which are generated by norms, so that for each of those topologies, tau, there is a set, Utau, that is open, dense and locally compact under tau. When the family is a vector space this implies that the family is finite dimensional.Ph.D.MathematicsPure SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/132799/2/3058034.pd