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The thermistor problem is modeled as a coupled system of nonlinear elliptic equations. When the conductivity coefficient a(u) vanishes (u = temperature) one of the equations becomes degenerate; this situation is considered in the present paper. We establish the existence of a weak solution and, under some special Dirichlet and Neumann boundary conditions, analyze the structure of the set {a(u) = 0} and also prove uniqueness.

The thermistor problem for conductivity which vanishes at large temperature