He completed his Ph.D. at Indiana University in 1941; his dissertation, titled On the Structure of the group of p-adic l-units, was written under the supervision of Emil Artin.
Gilbarg was co-author, together with his student Neil Trudinger, of the book Elliptic Partial Differential Equations of Second Order. Besides Trudinger, Gilbarg's doctoral students include Jerald Ericksen and James Serrin.
