  The complete set of (field) equations for shells of arbitrary, even changing,
causal character are derived in arbitrary dimension. New equations that seem to
have never been considered in the literature emerge, even in the traditional
cases of everywhere non-null, or everywhere null, shells. In the latter case
there arise field equations for some degrees of freedom encoded exclusively in
the distributional part of the Weyl tensor. For non-null shells the standard
Israel equations are recovered but not only, the additional relations
containing also relevant information. The results are applicable to a
widespread literature on domain walls, branes and braneworlds, gravitational
layers, impulsive gravitational waves, and the like. Moreover, they are of a
geometric nature, and thus they can be used in any theory based on a Lorentzian
manifold.
