On a Cahn-Hilliard model for phase separation with elastic misfit

Existence of solutions to a Cahn-Hilliard system taking elastic stresses into account is shown. The analysis is hindered by a logarithmic singularity and a quadratic term in the displacement gradient. This makes careful a priori estimates for both terms necessary. In particular, a global version of L-P-estimates for gradients of nonlinear elliptic systems is shown in order to control the logarithmic singularity. (c) 2005 Elsevier SAS. All rights reserved.