Models for growth of heterogeneous sandpiles via Mosco convergence
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)| n...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_09217134_v78_n1-2_p11_Bocea |
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todo:paper_09217134_v78_n1-2_p11_Bocea2023-10-03T15:45:40Z Models for growth of heterogeneous sandpiles via Mosco convergence Bocea, M. Mihǎilescu, M. Pérez-Llanos, M. Bocea, M. 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 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_09217134_v78_n1-2_p11_Bocea |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
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 |
| spellingShingle |
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 Bocea, M. Mihǎilescu, M. Pérez-Llanos, M. Bocea, M. Models for growth of heterogeneous sandpiles via Mosco convergence |
| topic_facet |
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 |
| description |
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. |
| format |
JOUR |
| author |
Bocea, M. Mihǎilescu, M. Pérez-Llanos, M. Bocea, M. |
| author_facet |
Bocea, M. Mihǎilescu, M. Pérez-Llanos, M. Bocea, M. |
| author_sort |
Bocea, M. |
| title |
Models for growth of heterogeneous sandpiles via Mosco convergence |
| title_short |
Models for growth of heterogeneous sandpiles via Mosco convergence |
| title_full |
Models for growth of heterogeneous sandpiles via Mosco convergence |
| title_fullStr |
Models for growth of heterogeneous sandpiles via Mosco convergence |
| title_full_unstemmed |
Models for growth of heterogeneous sandpiles via Mosco convergence |
| title_sort |
models for growth of heterogeneous sandpiles via mosco convergence |
| url |
http://hdl.handle.net/20.500.12110/paper_09217134_v78_n1-2_p11_Bocea |
| work_keys_str_mv |
AT boceam modelsforgrowthofheterogeneoussandpilesviamoscoconvergence AT mihailescum modelsforgrowthofheterogeneoussandpilesviamoscoconvergence AT perezllanosm modelsforgrowthofheterogeneoussandpilesviamoscoconvergence AT boceam modelsforgrowthofheterogeneoussandpilesviamoscoconvergence |
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1807317501629956096 |