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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| Autores principales: | , , |
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| Formato: | JOUR |
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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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| Sumario: | 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. |
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