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MiS Preprint
2/1999
Uniform Lipschitz estimates for extremals of singularly perturbed nonconvex functionals
Stefan Müller
Abstract
Uniform Lipschitz estimates are established for stationary points of $\int_\Omega F(Du) + \varepsilon^2 (\delta u)^2 dx $, where F approaches a strongly elliptic quadratic form at infinity. This generalizes work of Chipot and Evans who considered the case $\varepsilon = 0$ for minimizers. Applications to variational models of solid - solid phase transitions are discussed.
