Quantitative Estimates of the Field Excited by an Emitter in the Narrow Region Between Two Strictly Convex Inclusions in Two Dimensions

RESUMO

We consider the field enhancement due to the presence of an emitter of the dipole type near two perfectly conducting inclusions with $C^{2,\gamma}$ boundaries in two dimensions. We derive estimates of field enhancement in the narrow region and prove that the field is enhanced by a factor $\varepsilon^{-1/2}$ in the region far from the emitter. We construct a harmonic barrier to control the dipole term instead of using the Kelvin transformation. We also study how the location of the emitter affects the field on the shortest line segment connecting two inclusions.