Displaying similar documents to “Regularity of optimal shapes for the Dirichlet’s energy with volume constraint”

Some regularity results for minimal crystals

L. Ambrosio, M. Novaga, E. Paolini (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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We introduce an intrinsic notion of perimeter for subsets of a general Minkowski space ( i . e . a finite dimensional Banach space in which the norm is not required to be even). We prove that this notion of perimeter is equivalent to the usual definition of surface energy for crystals and we study the regularity properties of the minimizers and the quasi-minimizers of perimeter. In the two-dimensional case we obtain optimal regularity results: apart from a singular set (which is ℋ 1 -negligible...

Collisions and fractures: a model in S ⁢ B ⁢ D

Elena Bonetti, Michel Frémond (2004)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We investigate collisions (assumed to be instantaneous) and fractures of three-dimensional solids. Equations of motion and constitutive laws provide a set of partial differential equations, whose corresponding variational problem may be solved in the space of special functions with bounded deformations ( S ⁢ B ⁢ D ), exploiting the direct method of calculus of variations.

Design-dependent loads in topology optimization

Blaise Bourdin, Antonin Chambolle (2003)

ESAIM: Control, Optimisation and Calculus of Variations

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We present, analyze, and implement a new method for the design of the stiffest structure subject to a pressure load or a given field of internal forces. Our structure is represented as a subset S of a reference domain, and the complement of S is made of two other “phases”, the “void” and a fictitious “liquid” that exerts a pressure force on its interface with the solid structure. The problem we consider is to minimize the compliance of the structure S , which is the total work of the...