L∞ energies on discontinuous functions

Roberto Alicandro; Andrea Braides; Marco Cicalese

L^∞ energies on discontinuous functions

Roberto Alicandro, Andrea Braides, Marco Cicalese

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

2 Scopus citations

Abstract

We study necessary and sufficient conditions for the lower-semicontinuity of one-dimensional energies defined on (BV and) SBV of the model form F(u) = sup f (u′) V sup g ([u]), and prove a relaxation theorem. We apply these results to the study of problems with Dirichlet boundary conditions, highlighting a complex behaviour of solutions. We draw a comparison with the parallel theory for integral energies on SBV.

Original language	English
Pages (from-to)	905-928
Number of pages	24
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	12
Issue number	5
State	Published - May 2005
Externally published	Yes

Keywords

Functions of bounded variation
L energies
Lower semicontinuity

Cite this

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title = "L∞ energies on discontinuous functions",

abstract = "We study necessary and sufficient conditions for the lower-semicontinuity of one-dimensional energies defined on (BV and) SBV of the model form F(u) = sup f (u′) V sup g ([u]), and prove a relaxation theorem. We apply these results to the study of problems with Dirichlet boundary conditions, highlighting a complex behaviour of solutions. We draw a comparison with the parallel theory for integral energies on SBV.",

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author = "Roberto Alicandro and Andrea Braides and Marco Cicalese",

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volume = "12",

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journal = "Discrete and Continuous Dynamical Systems- Series A",

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T1 - L∞ energies on discontinuous functions

AU - Alicandro, Roberto

AU - Braides, Andrea

AU - Cicalese, Marco

PY - 2005/5

Y1 - 2005/5

N2 - We study necessary and sufficient conditions for the lower-semicontinuity of one-dimensional energies defined on (BV and) SBV of the model form F(u) = sup f (u′) V sup g ([u]), and prove a relaxation theorem. We apply these results to the study of problems with Dirichlet boundary conditions, highlighting a complex behaviour of solutions. We draw a comparison with the parallel theory for integral energies on SBV.

AB - We study necessary and sufficient conditions for the lower-semicontinuity of one-dimensional energies defined on (BV and) SBV of the model form F(u) = sup f (u′) V sup g ([u]), and prove a relaxation theorem. We apply these results to the study of problems with Dirichlet boundary conditions, highlighting a complex behaviour of solutions. We draw a comparison with the parallel theory for integral energies on SBV.

KW - Functions of bounded variation

KW - L energies

KW - Lower semicontinuity

UR - http://www.scopus.com/inward/record.url?scp=18144362849&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:18144362849

SN - 1078-0947

VL - 12

SP - 905

EP - 928

JO - Discrete and Continuous Dynamical Systems- Series A

JF - Discrete and Continuous Dynamical Systems- Series A

IS - 5

ER -

L^∞ energies on discontinuous functions

Abstract

Keywords

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