Abstract
In this paper we prove that solutions to an elliptic system of partial diVerential equations in divergence form whose boundary values are the restriction of a diVeomorphism of de- gree one onto a convex domain in two dimensions are mappings whose diVerential has a nonnegative determinant. Under appro- priate regularity assumptions on the domain, the boundary val- ues, and the coeYcients of the elliptic system, it is shown that so- lutions are diVeomorphisms whose diVerential has a strictly pos- itive determinant. We also describe applications of our results to problems arising in homogenization.
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