Aperiodic fractional obstacle problems

被引：15

作者：

Focardi, Matteo ^{[1
]}

机构：

[1] Dipartimento Matemat Ulisse Dini, I-50134 Florence, Italy

来源：

ADVANCES IN MATHEMATICS | 2010年 / 225卷 / 06期

关键词：

Obstacle problems; Non-local energies; Delone sets of points; Gamma-convergence; PERFORATED NONLINEAR MEDIA; PHASE-FIELD MODEL; STOCHASTIC HOMOGENIZATION; ASYMPTOTIC ANALYSIS; VARIABLE ORDER; GAMMA-LIMIT; REGULARITY; OPERATORS; DISLOCATIONS; INEQUALITIES;

D O I：

10.1016/j.aim.2010.06.014

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We determine the asymptotic behavior of (bilateral) obstacle problems for fractional energies in rather general aperiodic settings via Gamma-convergence arguments. As further developments we consider obstacles with random sizes and shapes located on points of standard lattices, and the case of random homothetics obstacles centered on random De lone sets of points. Obstacle problems for non-local energies occur in several physical phenomena, for which our results provide a description of the zeroth order asymptotic behavior. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：3502 / 3544

页数：43

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