Radio, X-ray, and gamma-ray observations provide us with strong evidence of particle acceleration to multi-TeV energies in various astrophysical sources. Diffusive shock acceleration is one of the most successful models explaining the presence of such high-energy particles. We discuss the impact of inverse Compton losses on the shock acceleration of electrons that takes place in radiation dominated environments, i.e. in regions where the radiation energy density exceeds that of the magnetic field. We perform a numerical calculation, including an energy-loss term in the transport equation of accelerated particles. We discuss the implications of this effect on the hard X-ray synchrotron and gamma-ray inverse Compton radiation, produced by shock-accelerated electrons in young supernova remnants in the presence of large radiation fields (e.g. in the Galactic centre). We also discuss possible implications of our results for clusters of galaxies and gamma-ray binaries. We demonstrate that the inverse Compton losses of electrons, in the Klein-Nishina regime, lead to spectra of ultra-relativistic electrons that may significantly differ from classical diffusive shock acceleration solution. The most prominent feature is the appearance of a pile-up in the spectrum around the cut-off energy.
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