I made a trip to the library and scanned the relevant pages from Miranda's 1955 book:

<A HREF="https://i.sstatic.net/CULF5xwr.jpg">page 152-153</A> and <A HREF="https://i.sstatic.net/w3WXueY8.jpg">page 154-155</A>

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)