This study is an attempt to generalize in dimension higher than two the mathematical results in [E. Bonnetier and A. Chambolle, SIAM J. Appl. Math., 62 (2002), pp. 1093-1121]. It is the study of a physical system whose equilibrium is the result of a competition between an elastic energy inside a domain and a surface tension, proportional to the perimeter of the domain. The domain is constrained to remain a subgraph. It is shown by Bonnetier and Chambolle that several phenomena appear at various scales as a result of this competition. In this paper, we focus on establishing a sound mathematical framework for this problem in a higher dimension. We also provide an approximation, based on a phase-field representation of the domain.

Interaction of a bulk and a surface energy with a geometrical constraint / Chambolle, A; Solci, Margherita. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - 39 (n. 1):(2007), pp. 77-102.

Interaction of a bulk and a surface energy with a geometrical constraint

SOLCI, Margherita
2007-01-01

Abstract

This study is an attempt to generalize in dimension higher than two the mathematical results in [E. Bonnetier and A. Chambolle, SIAM J. Appl. Math., 62 (2002), pp. 1093-1121]. It is the study of a physical system whose equilibrium is the result of a competition between an elastic energy inside a domain and a surface tension, proportional to the perimeter of the domain. The domain is constrained to remain a subgraph. It is shown by Bonnetier and Chambolle that several phenomena appear at various scales as a result of this competition. In this paper, we focus on establishing a sound mathematical framework for this problem in a higher dimension. We also provide an approximation, based on a phase-field representation of the domain.
2007
Interaction of a bulk and a surface energy with a geometrical constraint / Chambolle, A; Solci, Margherita. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - 39 (n. 1):(2007), pp. 77-102.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11388/78577
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