An approximation result for free discontinuity functionals by means of non-local energies

Luca Lussardi

doi:10.1002/mma.1019

An approximation result for free discontinuity functionals by means of non-local energies

Luca Lussardi

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

2 Citations (Scopus)

Abstract

We approximate, in the sense of Gamma-convergence, free discontinuity functionals with linear growth by a sequence of non-local integral functionals depending on the average of the gradient on small balls. The result extends to a higher dimension what is already proved in (Ann. Mat. Pura Appl. 2007; 186(4): 722–744), where there is the proof of the general one-dimensional case, and in (ESAIM Control Optim. Calc. Var. 2007; 13(1):135–162), where a particular n-dimensional case is treated. Moreover, we investigate whether it is possible to approximate a given free discontinuity functional by means of non-local energies.

Original language	English
Pages (from-to)	2133-2146
Number of pages	14
Journal	Mathematical Methods in the Applied Sciences
Volume	31
DOIs	https://doi.org/10.1002/mma.1019
Publication status	Published - 2008
Externally published	Yes

Keywords

free discontinuities
variational convergence

Access to Document

10.1002/mma.1019

Cite this

@article{3fba428c9b0a4965a2c907f774526ef5,

title = "An approximation result for free discontinuity functionals by means of non-local energies",

abstract = "We approximate, in the sense of Gamma-convergence, free discontinuity functionals with linear growth by a sequence of non-local integral functionals depending on the average of the gradient on small balls. The result extends to a higher dimension what is already proved in (Ann. Mat. Pura Appl. 2007; 186(4): 722–744), where there is the proof of the general one-dimensional case, and in (ESAIM Control Optim. Calc. Var. 2007; 13(1):135–162), where a particular n-dimensional case is treated. Moreover, we investigate whether it is possible to approximate a given free discontinuity functional by means of non-local energies.",

keywords = "free discontinuities, variational convergence, free discontinuities, variational convergence",

author = "Luca Lussardi",

year = "2008",

doi = "10.1002/mma.1019",

language = "English",

volume = "31",

pages = "2133--2146",

journal = "Mathematical Methods in the Applied Sciences",

issn = "0170-4214",

publisher = "John Wiley & Sons Limited:1 Oldlands Way, Bognor Regis, P022 9SA United Kingdom:011 44 1243 779777, EMAIL: cs-journals@wiley.co.uk, INTERNET: http://www.wiley.co.uk, Fax: 011 44 1243 843232 -Stuttgart: Teubner.",

}

TY - JOUR

T1 - An approximation result for free discontinuity functionals by means of non-local energies

AU - Lussardi, Luca

PY - 2008

Y1 - 2008

N2 - We approximate, in the sense of Gamma-convergence, free discontinuity functionals with linear growth by a sequence of non-local integral functionals depending on the average of the gradient on small balls. The result extends to a higher dimension what is already proved in (Ann. Mat. Pura Appl. 2007; 186(4): 722–744), where there is the proof of the general one-dimensional case, and in (ESAIM Control Optim. Calc. Var. 2007; 13(1):135–162), where a particular n-dimensional case is treated. Moreover, we investigate whether it is possible to approximate a given free discontinuity functional by means of non-local energies.

AB - We approximate, in the sense of Gamma-convergence, free discontinuity functionals with linear growth by a sequence of non-local integral functionals depending on the average of the gradient on small balls. The result extends to a higher dimension what is already proved in (Ann. Mat. Pura Appl. 2007; 186(4): 722–744), where there is the proof of the general one-dimensional case, and in (ESAIM Control Optim. Calc. Var. 2007; 13(1):135–162), where a particular n-dimensional case is treated. Moreover, we investigate whether it is possible to approximate a given free discontinuity functional by means of non-local energies.

KW - free discontinuities

KW - variational convergence

KW - free discontinuities

KW - variational convergence

UR - http://hdl.handle.net/10807/1978

U2 - 10.1002/mma.1019

DO - 10.1002/mma.1019

M3 - Article

SN - 0170-4214

VL - 31

SP - 2133

EP - 2146

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

ER -

An approximation result for free discontinuity functionals by means of non-local energies

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this