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

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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.