A. Braides, M. Gelli, M. Sigalotti, “The Passage from Nonconvex Discrete Systems to Variational Problems in Sobolev Spaces: The One-Dimensional Case”, Differential equations and dynamical systems, Collected papers. Dedicated to the 80th anniversary of academician Evgenii Frolovich Mishchenko, Trudy Mat. Inst. Steklova, 236, Nauka, MAIK «Nauka/Inteperiodika», M., 2002, 408–427; Proc. Steklov Inst. Math., 236 (2002), 395

Trudy Matematicheskogo Instituta imeni V.A. Steklova

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Forthcoming papers
	Archive
	Impact factor
	Guidelines for authors
	License agreement

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

Trudy Mat. Inst. Steklova:
Year:
Volume:
Issue:
Page:
	Find

Personal entry:
Login:
Password:
	Save password
	Enter
	Forgotten password?
	Register

Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2002, Volume 236, Pages 408–427 (Mi tm312)

This article is cited in 11 scientific papers (total in 11 papers)

The Passage from Nonconvex Discrete Systems to Variational Problems in Sobolev Spaces: The One-Dimensional Case

A. Braides^ab, M. Gelli^ab, M. Sigalotti^a

^a International School for Advanced Studies (SISSA)
^b Università degli Studi di Roma — Tor Vergata

Full-text PDF (237 kB) Citations (11)

References:

PDF

HTML

Abstract: We treat the problem of the description of the limits of discrete variational problems with long-range interactions in a one-dimensional setting. Under some polynomial-growth condition on the energy densities, we show that it is possible to define a local limit problem on a Sobolev space described by a homogenization formula. We give examples to show that, if the growth conditions are not uniformly satisfied, then the limit problem may be of a nonlocal form or with multiple densities.

Received in December 2000

Bibliographic databases:

UDC: 517.9

Language: English

Citation: A. Braides, M. Gelli, M. Sigalotti, “The Passage from Nonconvex Discrete Systems to Variational Problems in Sobolev Spaces: The One-Dimensional Case”, Differential equations and dynamical systems, Collected papers. Dedicated to the 80th anniversary of academician Evgenii Frolovich Mishchenko, Trudy Mat. Inst. Steklova, 236, Nauka, MAIK «Nauka/Inteperiodika», M., 2002, 408–427; Proc. Steklov Inst. Math., 236 (2002), 395–414

Citation in format AMSBIB

\Bibitem{BraGelSig02}

\by A.~Braides, M.~Gelli, M.~Sigalotti

\paper The Passage from Nonconvex Discrete Systems to Variational Problems in Sobolev Spaces: The One-Dimensional Case

\inbook Differential equations and dynamical systems

\bookinfo Collected papers. Dedicated to the 80th anniversary of academician Evgenii Frolovich Mishchenko

\serial Trudy Mat. Inst. Steklova

\yr 2002

\vol 236

\pages 408--427

\publ Nauka, MAIK «Nauka/Inteperiodika»

\publaddr M.

\mathnet{http://mi.mathnet.ru/tm312}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1931042}

\zmath{https://zbmath.org/?q=an:1023.49009}

\transl

\jour Proc. Steklov Inst. Math.

\yr 2002

\vol 236

\pages 395--414

Linking options:

https://www.mathnet.ru/eng/tm312

https://www.mathnet.ru/eng/tm/v236/p408

This publication is cited in the following 11 articles:

Braides A., Kreutz L., “An Integral-Representation Result For Continuum Limits of Discrete Energies With Multibody Interactions”, SIAM J. Math. Anal., 50:2 (2018), 1485–1520
Schaeffner M., Schloemerkemper A., “On Lennard-Jones Systems With Finite Range Interactions and Their Asymptotic Analysis”, Netw. Heterog. Media, 13:1 (2018), 95–118
Braides A., Solci M., “Asymptotic analysis of Lennard-Jones systems beyond the nearest-neighbour setting: A one-dimensional prototypical case”, Math. Mech. Solids, 21:8 (2016), 915–930
Alicandro R., Ansini N., “a Variational Model of Interaction Between Continuum and Discrete Systems”, Math. Models Meth. Appl. Sci., 24:10 (2014), 1957–2008
Alicandro R., Braides A., Cicalese M., “Continuum limits of discrete thin films with superlinear growth densities”, Calc. Var. Partial Differential Equations, 33:3 (2008), 267–297
Braides A., Cicalese M., “Surface energies in nonconvex discrete systems”, Math. Models Methods Appl. Sci., 17:7 (2007), 985–1037
Blanc X., Le Bris C., Lions P.-L., “Atomistic to continuum limits for computational materials science”, M2AN Math. Model. Numer. Anal., 41:2 (2007), 391–426
Alicandro R., Braides A., Cicalese M., “Phase and anti-phase boundaries in binary discrete systems: a variational viewpoint”, Netw. Heterog. Media, 1:1 (2006), 85–107
Alicandro R., Cicalese M., “A general integral representation result for continuum limits of discrete energies with superlinear growth”, SIAM J. Math. Anal., 36:1 (2004), 1–37
Braides A., Gelli M.S., “The passage from discrete to continuous variational problems: A nonlinear homogenization process - Continuum limits with bulk and surface energies”, Nonlinear Homogenization and its Applications to Composites, Polycrystals and Smart Materials, NATO Science Series, Series II: Mathematics, Physics and Chemistry, 170, 2004, 45–63
Paroni R., “From discrete to continuum: A Young measure approach”, Z. Angew. Math. Phys., 54:2 (2003), 328–348

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Труды Математического института имени В. А. Стеклова

Proceedings of the Steklov Institute of Mathematics

Statistics & downloads:
Abstract page:	377
Full-text PDF :	139
References:	74

Registration to the website

Logotypes