References
J. Hadamard, C. R.144 (1907), p. 1092.
L. Lichtenstein, Math. Annalen69 (1910), p. 514, has given a satisfactory proof in the elliptic case. However, his method is advanced and his functionF can not be analytic.
W. F. Osgood, Annals of Math., Ser. 2,2 (1900–1901), p. 125, footnote.
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Haviland, E.K. A note on the extremal surfaces in the calculus of variations. Math Z 38, 465–467 (1934). https://doi.org/10.1007/BF01170646
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DOI: https://doi.org/10.1007/BF01170646