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The Crab nebula is one of the most efficient accelerators in the Galaxy and the only galactic source showing direct evidence of PeV particles. In spite of this, the physical process behind such effective acceleration is still a deep mystery. While particle acceleration, at least at the highest energies, is commonly thought to occur at the pulsar wind termination shock, the properties of the upstream flow are thought to be non-uniform along the shock surface, and important constraints on the mechanism at work come from exact knowledge of where along this surface particles are being accelerated. Here we use axisymmetric relativistic magnetohydrodynamic simulations to obtain constraints on the acceleration site(s) of particles of different energies in the Crab nebula. Various scenarios are considered for the injection of particles responsible for synchrotron radiation in the different frequency bands, radio, optical and X-rays. The resulting emission properties are compared with available data on the multiwavelength time variability of the inner nebula. Our main result is that the X-ray emitting particles are accelerated in the equatorial region of the pulsar wind. Possible implications on the nature of the acceleration mechanism are discussed. [ABSTRACT FROM AUTHOR]