In this diploma thesis, we present a thorough investigation of the Vavilov-Cerenkov (VC) effect and its application to the detection of ultrahigh energyneutrinos. Neutrinos have no net charge and cannot emit VC radiation(VCR) but when they interact with a stationary medium such radiation isproduced by the Askar'yan effect. It has been proposed to use the lunarregolith as a detector material for such neutrino interactions, but in orderto do so, the VCR emitted from neutrino interactions has to be filtered outfrom that of other energetic particles impinging upon and penetrating intothe lunar surface. Since the principal difference between these emissions isdependent on the depth at which they occur, any boundary effects dependenton the distance from the point of emission to the surface is of interest.Therefore we examine the behavior of VCR near dielectric boundaries withextra care, both analytically and numerically. In order to keep the physicalpicture as clear as possible the analytical derivations are conducted in thetemporal domain. The boundary problem is studied both with respect tothe Maxwell boundary conditions and the method of images. In order toverify the analytic results and to make further investigations, a numericalMaxwell solver for the general VCR problem was constructed. The analyticand numeric results are then compared and proven to be equivalent. TheMaxwell solver is used to study the boundary problem and it is shown thatthe VCR emitted in a medium near the surface does not depend on the distanceto the surface in the same way as the opposite problem with a chargeabove the medium. In the case of a charge distribution traveling partiallyon both sides of the boundary some frequency dependent effects are shown.