[41] Crelle's Journal, vol. 84 (1878), and Atti d. Reale Acad. di Napoli, 1880.
[42] Leipzig, 1897. Cf. especially Abschnitt I, Chaplets 2 and 3.
[43] Symmetrie der regelmässigen Systeme von Figuren, 1890.
[44] Krystallsysteme und Krystallstruktur, Leipzig, 1891.
[45] Math. Annalen, vol. 53.
[46] Math. Annalen, vol. 28.
19. ARE THE SOLUTIONS OF REGULAR PROBLEMS IN THE CALCULUS OF VARIATIONS ALWAYS NECESSARILY ANALYTIC?
One of the most remarkable facts in the elements of the theory of analytic functions appears to me to be this: That there exist partial differential equations whose integrals are all of necessity analytic functions of the independent variables, that is, in short, equations susceptible of none but analytic solutions. The best known partial differential equations of this kind are the potential equation
and certain linear differential equations investigated by Picard;[47] also the equation