Calculus of Variations and Geometric Measure Theory
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J. Lamboley - M. Pierre

Structure of shape derivatives around irregular domains and applications

created by lamboley on 21 May 2016


Accepted Paper

Inserted: 21 may 2016
Last Updated: 21 may 2016

Journal: Journal of Convex Analysis
Volume: 14
Number: 4
Pages: 807--822
Year: 2007


In this paper, we describe the structure of shape derivatives around sets which are only assumed to be of finite perimeter in $\mathbb{R}^N$. This structure allows us to define a useful notion of positivity of the shape derivative and we show it implies its continuity with respect to the uniform norm when the boundary is Lipschitz (this restriction is essentially optimal). We apply this idea to various cases including the perimeter-type functionals for convex and pseudo-convex shapes or the Dirichlet energy of an open set.


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