Univalent solutions of an elliptic system of partial differential equations arising in homogenization
Patricia A. Bauman, Antonella Marini, Vincenzo Nesi · Indiana University Mathematics Journal · 2001
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.