  We study the initial boundary value problem for a heat equation in a domain
containing a thin layer. The thermal conductivity of the layer is drastically
different from that of the bulk of the domain; moreover, the layer is
anisotropic and ``optimally aligned" in the sense that the normal direction in
the layer is always an eigenvector of the thermal tensor. To reveal the effects
of the layer, we regard it as a thickless surface on which ``effective boundary
conditions" (EBCs) are satisfied by the limit of solutions of the initial
boundary value problem as the thickness of the layer shrinks to zero. These
EBCs are rich in variety and type, including some nonstandard ones such as the
Dirichlet-to-Neumann mapping and the fractional Laplacian.
