Elliptic Variational Problems on Constricted Networks with Applications to Ginzburg-Landau Theory

Peter Sternberg, Indiana University

I will analyze variational problems set on a network of thin constricted tubes. In the asymptotic regime where the tubes collapse to a graph, one can identify a one dimensional variational problem with interesting natural boundary conditions at the nodes which in particular encourage jumps in the (limit of) minimizers across the various branches of the graph. An application to tunneling across weak links in a superconductor will be discussed.