Abstract:We are concerned with the field concentration between two nearlytouching inclusions with high-contrast material parameters, which is a central topic in the theory of composite materials. The degree of concentration is characterised by the blowup rate of the gradient of the underlying field. In this paper, we derive optimal gradient estimates for the wave field of the 3-D Helmholtz system in the quasi-static regime. There are two salient features of our results that are new to the literature. First, we cover al… Show more
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