  We discuss one of the many topics that illustrate the interaction of Blaine
Lawson's deep geometric and analytic insights. The first author is extremely
grateful to have had the pleasure of collaborating with Blaine over many
enjoyable years. The topic to be discussed concerns the fruitful interplay
between nonlinear potential theory; that is, the study of subharmonics with
respect to a general constraint set in the 2-jet bundle and the study of
subsolutions and supersolutions of a nonlinear (degenerate) elliptic PDE. The
main results include (but are not limited to) the validity of the comparison
principle and the existence and uniqueness to solutions to the relevant
Dirichlet problems on domains which are suitably "pseudoconvex". The methods
employed are geometric and flexible as well as being very general on the
potential theory side, which is interesting in its own right. Moreover, in many
important geometric contexts no natutral operator may be present. On the other
hand, the potential theoretic approach can yield results on the PDE side in
terms of non standard structual conditions on a given differential operator.
