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On conformal variational problems and free boundary continua

Stephen Marsland ; Robert I McLachlan ; Klas Modin (Institutionen för matematiska vetenskaper, matematik) ; Matthew Perlmutter
Journal of Physics A: Mathematical and Theoretical (1751-8113). Vol. 47 (2014), 14, p. Art. no. 145204.
[Artikel, refereegranskad vetenskaplig]

We develop a framework for deriving governing partial differential equations for variational problems on spaces of conformal mappings. The main motivation is to obtain differential equations for the conformal motion of free boundary continua, of interest in image and shape registration. A fundamental tool in the paper, the Hodge–Morrey–Friedrichs decompositions of differential forms on manifolds with boundaries, is used to identify the orthogonal complement of the subspace of conformal mappings. A detailed presentation of these decompositions is included in the paper.

Nyckelord: calculus of variations; conformal embeddings; free boundary continua; Hodge decomposition of vector fields and differential forms



Denna post skapades 2014-03-27. Senast ändrad 2015-04-27.
CPL Pubid: 195786

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Geometri

Chalmers infrastruktur