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Journal of Convex Analysis 07 (2000), No. 2, 209--242
Copyright Heldermann Verlag 2000

A Two-Dimensional Variational Model for the Equilibrium Configuration of an Incompressible, Elastic Body with a Three-Well Elastic Potential

Martin Fuchs
Fachbereich Mathematik, Universität des Saarlandes, 66041 Saarbrücken, Germany

Gregory Seregin
Steklov Math. Institute, 191011 St. Petersburg, Russia

We consider a geometrically linear variational model in two space dimensions for an incompressible, elastic body whose elastic potential has exactly three wells corresponding to one austenitic and to two martensitic phases. Passing to the dual problem we show that the stress tensor is weakly differentiable on the interior of the domain and in addition Hölder continuous on any subset of the union of the pure phases.

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