  We analyse a family of mutually orthogonal polynomials on the unit ball with
respect to an inner product which involves the outward normal derivatives on
the sphere. Using their representation in terms of spherical harmonics,
algebraic and analytic properties will be deduced. First, we deduce explicit
connection formulas relating classical multivariate ball polynomials and our
family of Sobolev orthogonal polynomials. Then explicit representations for the
norms and the kernels will be obtained. Finally, the asymptotic behaviour of
the corresponding Christoffel functions is studied.
