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Abstract
We consider the Γ-limit of a highly oscillatory Riemannian metric length functional as its period tends to 0. The metric coefficient takes values in either {1, ∞} or {1, βε-g} where β, ε > 0 and p ∈ (0, ∞). We find that for a large class of metrics, in particular those metrics whose surface of discontinuity forms a differentiable manifold, the Γ-limit exists, as in the case of a uniformly bounded sequence of metrics. However, the existence of the Γ-limit for the corresponding boundary value problem depends on the value of p. Specifically, we show that the power p = 1 is critical in that the Γ-limit exists for p < 1, whereas it ceases to exist for p = 1. The results here have applications in both nonlinear optics and the effective description of a Hamiltonian particle in a discontinuous potential.
Original language | English |
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Pages (from-to) | 411-426 |
Number of pages | 16 |
Journal | Discrete and Continuous Dynamical Systems - Series A |
Volume | 35 |
Issue number | 1 |
Early online date | 1 Aug 2014 |
DOIs | |
Publication status | Published - Jan 2015 |
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Dive into the research topics of 'On the Γ-limit for a non-uniformly bounded sequence of two-phase metric functionals'. Together they form a unique fingerprint.Projects
- 1 Finished
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Analysis of the Effective Long Time-Behaviour of Molecule Systems
Zimmer, J. (PI)
Engineering and Physical Sciences Research Council
16/12/13 → 15/12/16
Project: Research council