Bmo and Uniform Estimates for Multi–well Problems
نویسندگان
چکیده
We establish optimal local regularity results for vector-valued extremals and minimizers of variational integrals whose integrand is the squared distance function to a compact setK in matrix space MN×n. The optimality is illustrated by explicit examples showing that, in the nonconvex case, minimizers need not be locally Lipschitz. This is in contrast to the case when the set K is suitably convex, where we show that extremals are locally Lipschitz continuous. The results rely on the special structure of the integrand and elementary Cordes–Nirenberg type estimates for elliptic systems. 1991Mathematics Subject Classification. 49Q20, 35B05.
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