Interface response theory of continuous composite systems

The interface response theory was recently presented for any composite material in discrete spaces. However, continuous spaces are even more used than discrete ones. For example, elasticity theory uses the usual three-dimensional continuous space, while lattice dynamics uses a 3D-discrete space. Similarly, the continuous Schrِdinger equation can be solved within the continuous space for free electrons and in the pseudopotential formulations or within the atomic discrete space in the tight-binding approaches. The continuum limits of the main equations of the interface response theory of discrete composite systems will be reported in their most general forms. A general application to elasticity theory, will illustrate this report.