Abstract
We study solutions of the two-well problem, i.e., maps which satisfy ueSO(n)A∪SO(n)B a.c. in Ω ⊂ℝ n , where A and B are n×n matrices with positive determinants. This problem arises in the study of microstructure in solid-solid phase transitions. Under the additional hypothesis that the set E where the gradient lies in SO(n) A has finite perimeter, we show that u is locally only a function of one variable and that the boundary of E consists of (subsets of) hyperplanes which extend to ∂Ω and which do not intersect in Ω. This may not be the case if the assumption on E is dropped. We also discuss applications of this result to magnetostrictive materials.
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