This article is cited 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<sup>a

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

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.

UDC: 517.9

Received in December 2000

Language: English

 English version: Proceedings of the Steklov Institute of Mathematics, 2002, 236, 395–414

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