On the decay rate of solutions of the wave equation in domains with star-shaped boundaries

One studies the large-time decay rate of the weighted energy of solutions of the first mixed problem for the wave equation in domains with smooth boundaries which are star-shaped with respect to the origin. Estimates are established for solutions of the first boundary-value problem for the Helmholtz equation in the upper half-plane. __________ Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 26, pp. 390–406, 2007.