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Dilaton gravity with general brane localized interactions is investigated.Models with corrections up to arbitrary order in field derivatives areconsidered. Effective gravitational equations of motion at the brane arederived in the covariant approach. Dependence of such brane equations on thebulk quantities is discussed. It is shown that the number of the bulkindependent brane equations of motion depends strongly on the symmetriesassumed for the model and for the background. Examples with two and fourderivatives of the fields are presented in more detail.

Higher order dilaton gravity: brane equations of motion in the covariant formulation