The generalized Jang equation was introduced in an attempt to prove the
Penrose inequality in the setting of general initial data for the Einstein
equations. In this paper we give an extensive study of this equation, proving
existence, regularity, and blow-up results. In particular, precise asymptotics
for the blow-up behavior are given, and it is shown that blow-up solutions are
not unique.Comment: 33 pages; final versio
