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We present the theory of damping of low-energy excitations of a trapped Bosecondensate at finite temperatures, where the damping is provided by theinteraction of these excitations with the thermal excitations. We emphasize thekey role of stochastization in the behavior of the thermal excitations fordamping in non-spherical traps. The damping rates of the lowest excitations,following from our theory, are in fair agreement with the data of recent JILAand MIT experiments. The damping of quasiclassical excitations is determined bythe condensate boundary region, and the result for the damping rate isdrastically different from that in a spatially homogeneous gas.Comment: 10 pages RevTeX, correction of the misprints and addition of the  sentence clarifying the result for quasiclassical excitationscorrection of  the misprints and addition of the sentence clarifying the result for  quasiclassical excitation

Damping of Low-Energy Excitations of a Trapped Bose-Einstein Condensate at Finite Temperatures