A note on the smoothness of energy-minimizing incompressible deformations
Nirmalendu Chaudhuri
Abstract
In this note we prove that any W1,2 mapping u in the plane that minimizes an appropriate quasiconvex energy functional subject to the Jacobian constraint det u=1 a.e., are necessarily Lipschitz. Furthermore we show that the minimizers corresponding to uniformly convex energy are affine and give an example of non-affine minimizers subject to affine boundary data corresponding to a convex energy. We also discuss the regularity issues in dimension greater than or equal to 3.
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