$C^\infty$ regularity of the free boundary for a two-dimensional optimal compliance problem |
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Authors: | Antonin?Chambolle Email author" target="_blank">Christopher?J?LarsenEmail author |
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Institution: | (1) CEREMADE (CNRS UMR 7534), Université de Paris-Dauphine, 75775 Paris CEDEX 16, France;(2) Department of Mathematical Sciences, Worcester Polytechnic Institute, MA 01609 Worcester, USA |
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Abstract: | We study the regularizing effect of perimeter penalties for a problem of optimal compliance in two dimensions. In particular, we consider minimizers of where The sets
,
, and the force f are given. We show that if we consider only scalar valued u and constant
, or if we consider the elastic energy
, then
is
away from where
is pinned. In the scalar case, we also show that, for any
of class
,
is
. The proofs rely on a notion of weak outward curvature of
, which we can bound without considering properties of the minimizing fields, together with a bootstrap argument.Received: 5 March 2002, Accepted: 3 September 2002, Published online: 17 December 2002 |
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Keywords: | |
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