An extension result for generalised special functions of bounded deformation

Filippo Cagnetti; Antonin Chambolle; Matteo Perugini; Lucia Scardia

An extension result for generalised special functions of bounded deformation

Filippo Cagnetti, Antonin Chambolle, Matteo Perugini, Lucia Scardia

Research output: Contribution to journal › Article › peer-review

Abstract

We show an extension result for generalised special functions of bounded deformation (GSBDp, for every p > 1) and any dimension n ≥ 2. The proof is based on a recent result of F. Cagnetti, A. Chambolle, and L. Scardia, where it is shown that a function u in GSBDp with a “small” jump set coincides with a W1,p function, up to a small set whose perimeter and volume are controlled by the size of the jump of u.

Original language	English
Journal	Journal of Convex Analysis
Volume	28
Issue number	2
Early online date	2020
Publication status	Published - 2021

Keywords

Free-discontinuity problems
Functions of bounded deformation
Griffith’s energy

ASJC Scopus subject areas

Analysis
General Mathematics

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http://www.heldermann.de/JCA/JCA28/JCA282/jca28024.htm

Cite this

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title = "An extension result for generalised special functions of bounded deformation",

abstract = "We show an extension result for generalised special functions of bounded deformation (GSBDp, for every p > 1) and any dimension n ≥ 2. The proof is based on a recent result of F. Cagnetti, A. Chambolle, and L. Scardia, where it is shown that a function u in GSBDp with a “small” jump set coincides with a W1,p function, up to a small set whose perimeter and volume are controlled by the size of the jump of u.",

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author = "Filippo Cagnetti and Antonin Chambolle and Matteo Perugini and Lucia Scardia",

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language = "English",

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journal = "Journal of Convex Analysis",

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AU - Cagnetti, Filippo

AU - Chambolle, Antonin

AU - Perugini, Matteo

AU - Scardia, Lucia

PY - 2021

Y1 - 2021

N2 - We show an extension result for generalised special functions of bounded deformation (GSBDp, for every p > 1) and any dimension n ≥ 2. The proof is based on a recent result of F. Cagnetti, A. Chambolle, and L. Scardia, where it is shown that a function u in GSBDp with a “small” jump set coincides with a W1,p function, up to a small set whose perimeter and volume are controlled by the size of the jump of u.

AB - We show an extension result for generalised special functions of bounded deformation (GSBDp, for every p > 1) and any dimension n ≥ 2. The proof is based on a recent result of F. Cagnetti, A. Chambolle, and L. Scardia, where it is shown that a function u in GSBDp with a “small” jump set coincides with a W1,p function, up to a small set whose perimeter and volume are controlled by the size of the jump of u.

KW - Free-discontinuity problems

KW - Functions of bounded deformation

KW - Griffith’s energy

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M3 - Article

SN - 0944-6532

VL - 28

JO - Journal of Convex Analysis

JF - Journal of Convex Analysis

IS - 2

ER -

An extension result for generalised special functions of bounded deformation

Abstract

Keywords

ASJC Scopus subject areas

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