I made a trip to the library and scanned the relevant pages from Miranda's 1955 book:
page 152-153page 152-153 and page 154-155page 154-155
the references are:
[3] J. Leray, J.Math. pures et appl. 17, 89-104 (1938)
[8] R. Cacciopoli, Rend.Acc.Lincei 22, 305-310 and 376-379 (1935).
[11] R. Cacciopoli, Giorn.Mat.Battaglini, 80, 186-212 (1950-51)