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Abstract:

In this paper we study the asymptotic behavior of several classes of power-law functionals involving variable exponents p n(·) →∞, via Mosco convergence. In the particular case p n(·)=np(·), we show that the sequence {H n} of functionals H n:L 2(R N)→[0,+∞] given by H n(u)=∫R Nλ(x) n/np(x) |∇u(x)| np(x)dx if u∈L 2(R N) ∩W 1,np(·)(R N), +∞ otherwise, converges in the sense of Mosco to a functional which vanishes on the set u∈L 2(R N): λ(x)|∇u| p(x)≤ 1 a.e. x∈R N and is infinite in its complement. We also provide an example of a sequence of functionals whose Mosco limit cannot be described in terms of the characteristic function of a subset of L 2(R N). As an application of our results we obtain a model for the growth of a sandpile in which the allowed slope of the sand depends explicitly on the position in the sample. © 2012 - IOS Press and the authors. All rights reserved.

Registro:

Documento: Artículo
Título:Models for growth of heterogeneous sandpiles via Mosco convergence
Autor:Bocea, M.; Mihǎilescu, M.; Pérez-Llanos, M.; Bocea, M.
Filiación:Department of Mathematics and Statistics, Loyola University Chicago, 1032 W. Sheridan Road, Chicago, IL 60660, United States
Department of Mathematics, University of Craiova, Craiova, Romania
Department of Mathematics, University of Texas at Austin, Austin, TX, United States
Departamento de Análisis Matemático, Universidad de Alicante, Alicante, Spain
Departamento de Matemática, FCEyN UBA, Ciudad Universitaria, Pab 1 (1428), Buenos Aires, Argentina
Palabras clave:Mosco convergence; power-law functionals; sandpile models; variable exponent spaces; Asymptotic behaviors; Characteristic functions; Functionals; Mosco-convergence; Power-law; Sand-pile models; Variable exponents; Asymptotic analysis; Sand
Año:2012
Volumen:78
Número:1-2
Página de inicio:11
Página de fin:36
DOI: http://dx.doi.org/10.3233/ASY-2011-1083
Título revista:Asymptotic Analysis
Título revista abreviado:Asymptotic Anal
ISSN:09217134
CODEN:ASANE
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09217134_v78_n1-2_p11_Bocea

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Citas:

---------- APA ----------
Bocea, M., Mihǎilescu, M., Pérez-Llanos, M. & Bocea, M. (2012) . Models for growth of heterogeneous sandpiles via Mosco convergence. Asymptotic Analysis, 78(1-2), 11-36.
http://dx.doi.org/10.3233/ASY-2011-1083
---------- CHICAGO ----------
Bocea, M., Mihǎilescu, M., Pérez-Llanos, M., Bocea, M. "Models for growth of heterogeneous sandpiles via Mosco convergence" . Asymptotic Analysis 78, no. 1-2 (2012) : 11-36.
http://dx.doi.org/10.3233/ASY-2011-1083
---------- MLA ----------
Bocea, M., Mihǎilescu, M., Pérez-Llanos, M., Bocea, M. "Models for growth of heterogeneous sandpiles via Mosco convergence" . Asymptotic Analysis, vol. 78, no. 1-2, 2012, pp. 11-36.
http://dx.doi.org/10.3233/ASY-2011-1083
---------- VANCOUVER ----------
Bocea, M., Mihǎilescu, M., Pérez-Llanos, M., Bocea, M. Models for growth of heterogeneous sandpiles via Mosco convergence. Asymptotic Anal. 2012;78(1-2):11-36.
http://dx.doi.org/10.3233/ASY-2011-1083