  Dilaton gravity with general brane localized interactions is investigated.
Models with corrections up to arbitrary order in field derivatives are
considered. Effective gravitational equations of motion at the brane are
derived in the covariant approach. Dependence of such brane equations on the
bulk quantities is discussed. It is shown that the number of the bulk
independent brane equations of motion depends strongly on the symmetries
assumed for the model and for the background. Examples with two and four
derivatives of the fields are presented in more detail.
