The minimum of quadratic functionals of the gradient on the set of convex functions
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چکیده
The minimum of quadratic functionals of the gradient on the set of convex functions ABSTRACT We study the innmum of functionals of the form R Mruru among all convex functions u 2 H 1 0 (() such that R jruj 2 = 1. (is a convex open subset of R N , and M is a given symmetric N N matrix.) We prove that this innmum is the smallest eigenvalue of M if is C 1. Otherwise the picture is more complicated. We also study the case of an x-dependent matrix M.
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تاریخ انتشار 2000