Work

Elasticae and inradius

Year: 2016

Type: preprint

Abstract: The elastic energy of a planar convex body is defined by $E(\Om)=\frac 12\,\int\_{\partial\Om} k^2(s)\,ds$where $k(s)$ is the curvature of the boundary. In this paper we are interested in the minimization problemof $E(\Om)$ with a constraint on the inradius of $\Om$. By contrast with all the other minimization problemsinvolving this elastic energy (with a perimeter, area, diameter or circumradius constraints) for which thesolution is always the disk, we prove here that the solution of this minimization problem is not the disk and we completely characterizeit in terms of elementary functions.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1608.00727

Authors: Henrot, Antoine, Mounjid, Othmane

Institutions: Centre National de la Recherche Scientifique, Institut Élie Cartan de Lorraine, Université de Lorraine, École Nationale Supérieure des Mines de Nancy

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Université de Lorraine, Agence Nationale de la Recherche

Awards: Shape Optimization, G6702880738

OpenAlex ID: W2950516385

Cites: 4

Cited by:

Related to: 20