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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2012
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| LEADER | 10994caa a22010817a 4500 | ||
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| 008 | 190411s2012 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-84857069128 | |
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| 100 | 1 | |a Bocea, M. | |
| 245 | 1 | 0 | |a Models for growth of heterogeneous sandpiles via Mosco convergence |
| 260 | |c 2012 | ||
| 270 | 1 | 0 | |m Bocea, M.; Department of Mathematics and Statistics, Loyola University Chicago, 1032 W. Sheridan Road, Chicago, IL 60660, United States; email: mbocea@luc.edu |
| 506 | |2 openaire |e Política editorial | ||
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| 520 | 3 | |a 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. |l eng | |
| 593 | |a Department of Mathematics and Statistics, Loyola University Chicago, 1032 W. Sheridan Road, Chicago, IL 60660, United States | ||
| 593 | |a Department of Mathematics, University of Craiova, Craiova, Romania | ||
| 593 | |a Department of Mathematics, University of Texas at Austin, Austin, TX, United States | ||
| 593 | |a Departamento de Análisis Matemático, Universidad de Alicante, Alicante, Spain | ||
| 593 | |a Departamento de Matemática, FCEyN UBA, Ciudad Universitaria, Pab 1 (1428), Buenos Aires, Argentina | ||
| 690 | 1 | 0 | |a MOSCO CONVERGENCE |
| 690 | 1 | 0 | |a POWER-LAW FUNCTIONALS |
| 690 | 1 | 0 | |a SANDPILE MODELS |
| 690 | 1 | 0 | |a VARIABLE EXPONENT SPACES |
| 690 | 1 | 0 | |a ASYMPTOTIC BEHAVIORS |
| 690 | 1 | 0 | |a CHARACTERISTIC FUNCTIONS |
| 690 | 1 | 0 | |a FUNCTIONALS |
| 690 | 1 | 0 | |a MOSCO-CONVERGENCE |
| 690 | 1 | 0 | |a POWER-LAW |
| 690 | 1 | 0 | |a SAND-PILE MODELS |
| 690 | 1 | 0 | |a VARIABLE EXPONENTS |
| 690 | 1 | 0 | |a ASYMPTOTIC ANALYSIS |
| 690 | 1 | 0 | |a SAND |
| 700 | 1 | |a Mihǎilescu, M. | |
| 700 | 1 | |a Pérez-Llanos, M. | |
| 700 | 1 | |a Bocea, M. | |
| 773 | 0 | |d 2012 |g v. 78 |h pp. 11-36 |k n. 1-2 |p Asymptotic Anal |x 09217134 |w (AR-BaUEN)CENRE-3856 |t Asymptotic Analysis | |
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