2-dimensional conductivity problem and quasiconformal mappings
                            
                            by
   
     Markku Miettinen and Kari Astala, University of Jyvaskyla, Finland


             JTB 120, 3:30pm  Monday, April 20, 1998


                          Abstract

We shall discuss a problem of finding the optimal bounds
on the conductivity of mixtures of nonisotropic crystals
in terms of their volume ratios only. Our study is based on a
breakthrough found by V. Nesi who obtained optimal bounds by applying
the optimal quasiconformal estimates established ealier by
K. Astala. Quasiconformal estimates turned out to
be a crucial tool in this connection, as optimal conductivity
problems can be modelled by elliptic variational integrals.


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