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Abstract
We consider the Γlimit 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 Γlimit exists, as in the case of a uniformly bounded sequence of metrics. However, the existence of the Γlimit 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 Γlimit 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 

Pages (fromto)  411426 
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 Γlimit for a nonuniformly bounded sequence of twophase metric functionals'. Together they form a unique fingerprint.Projects
 1 Finished

Analysis of the Effective Long TimeBehaviour of Molecule Systems
Zimmer, J. (PI)
Engineering and Physical Sciences Research Council
16/12/13 → 15/12/16
Project: Research council