We continue our analysis on functionals depending on the curvature of graphs of curves in high codimension Euclidean space. We deal with the “elastic” case, corresponding to a superlinear dependence on the pointwise curvature.We introduce the corresponding relaxed energy functional and prove an explicit representation formula. Different phenomena w.r.t. the “plastic” case, i.e. to the relaxation of the total curvature functional, are observed. A p-curvature functional is well-defined on continuous curves with finite relaxed energy, and the relaxed energy is given by the length plus the p-curvature. The wider class of graphs of one-dimensional BV-functions is treated.

Curvature-dependent energies: The elastic case / Acerbi, Emilio Daniele Giovanni; Mucci, Domenico. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 153(2016), pp. 7-34. [10.1016/j.na.2016.05.012]

Curvature-dependent energies: The elastic case

ACERBI, Emilio Daniele Giovanni;MUCCI, Domenico
2016

Abstract

We continue our analysis on functionals depending on the curvature of graphs of curves in high codimension Euclidean space. We deal with the “elastic” case, corresponding to a superlinear dependence on the pointwise curvature.We introduce the corresponding relaxed energy functional and prove an explicit representation formula. Different phenomena w.r.t. the “plastic” case, i.e. to the relaxation of the total curvature functional, are observed. A p-curvature functional is well-defined on continuous curves with finite relaxed energy, and the relaxed energy is given by the length plus the p-curvature. The wider class of graphs of one-dimensional BV-functions is treated.
Curvature-dependent energies: The elastic case / Acerbi, Emilio Daniele Giovanni; Mucci, Domenico. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 153(2016), pp. 7-34. [10.1016/j.na.2016.05.012]
File in questo prodotto:
File Dimensione Formato  
CurvElsevierP.pdf

accesso aperto

Descrizione: preprint, sostanzialmente identico allo stampato (reperibile online)
Tipologia: Documento in Pre-print
Licenza: Creative commons
Dimensione 364.82 kB
Formato Adobe PDF
364.82 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11381/2818225
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 4
  • ???jsp.display-item.citation.isi??? 4
social impact